200 questions · 180 minutes · −0.25 per wrong answer · Free
Answer: (C) 6
Regroup the left side as $(x - 2)^2 + (x - z)^2 + (y - z)^2 = 0$. A sum of squares of real numbers is zero only when each square is zero, so $x = 2$, $z = x = 2$ and $y = z = 2$, giving $x + y + z = 6$. The values 2, 8 and 10 do not satisfy all three conditions.
Answer: (A) $7\sqrt{3}$ cm
$\pi r^2 = 154$ gives $r^2 = 49$, so the circumradius is 7 cm. For an equilateral triangle the side equals $r\sqrt{3}$, so every side (and hence the 'longest') is $7\sqrt{3}$ cm. 7 cm is the radius itself, not the side, and 3·5 cm and 28 cm do not fit the formula.
Answer: (B) accb
Filling a, c, c, b gives abca a bcaab c aab c aa b ca = abca abca abca abca abca, the block 'abca' repeated five times. Any other choice breaks this repeating pattern; for example 'ccaa' puts c after 'abca' where the next block must start with a.
Answer: (D) 72, 96, 108
Multiplying by 12, the ratio $\frac{1}{2} : \frac{2}{3} : \frac{3}{4}$ becomes 6 : 8 : 9. The difference between greatest and smallest is 9k − 6k = 3k = 36, so k = 12 and the numbers are 72, 96, 108. The other sets are not in the ratio 6 : 8 : 9.
Answer: (C) ₹ 2,000
Interest on ₹ 1,200 at 5% for 4 years = 1200 × 5 × 4 / 100 = ₹ 240. The required sum P must satisfy P × 4 × 3 / 100 = 240, so P = ₹ 2,000. ₹ 1,000 or ₹ 1,500 would earn only ₹ 120 or ₹ 180, and ₹ 2,500 would earn ₹ 300.
Answer: (C) Plagiarism
Misappropriation is the dishonest taking of someone else's money; the matching wrong for writing is plagiarism, passing off someone else's writing as one's own. Theft and deception are general wrongs not specific to writing, and a mistake is not dishonest at all.
Answer: (B) 21 hours
The pipe fills $\frac{1}{3}$ of the tank per hour, while pipe and leak together fill $\frac{2}{7}$ per hour. The leak therefore empties $\frac{1}{3} - \frac{2}{7} = \frac{1}{21}$ per hour, i.e. the full tank in 21 hours. 12 or $10\frac{1}{2}$ hours would make the leak too strong to allow filling in $3\frac{1}{2}$ hours.
Answer: (C) 47
Total of 11 results = 11 × 32 = 352; first five total 5 × 27 = 135 and last five total 5 × 34 = 170. The sixth result is 352 − 135 − 170 = 47. The other values would make the overall total wrong.
Answer: (A) 10%
Candidates who passed in at least one subject = 60 + 70 − 40 = 90%. So those who failed in both = 100 − 90 = 10%. 40% and 30% are the shares who failed in English and in Maths taken one at a time, not those who failed in both.
Answer: (A) 265
In the diagram the Hindi circle contains 70 (Hindi only) + 65 (Hindi and Bengali) + 53 (all three) + 47 (Hindi and English) = 235 persons. Those who do not know Hindi are 500 − 235 = 265, which is also the sum of the remaining regions 120 + 62 + 83. 200, 255 and 201 miss one or more of these regions.
Answer: (A) $1 : \sqrt{3}$
Equating the curved surfaces, $2\pi r^2 = \pi r l$, so the slant height $l = 2r$. Then $h = \sqrt{l^2 - r^2} = \sqrt{3}r$, so $r : h = 1 : \sqrt{3}$. Option B reverses the ratio, and C and D come from using the wrong relation between $l$ and $h$.
Answer: (B) 64
The wrong total was 9 × 65 = 585, which is 76 − 67 = 9 too high. The correct total is 576, and 576 ÷ 9 = 64. 66 would follow from adding the error instead of subtracting it.
Answer: (A) 5
Interior and exterior angles add up to $180^\circ$, so in the ratio 3 : 2 the exterior angle is $72^\circ$. The number of sides is $360^\circ \div 72^\circ = 5$. A 10-sided polygon would have exterior angles of $36^\circ$, giving a ratio of 4 : 1.
Answer: (B) 28 minutes
For the same distance time is inversely proportional to speed; speed × 1·25 means time ÷ 1·25. So train B takes 35 ÷ 1·25 = 28 minutes. Simply cutting 25% of the time would wrongly give about 26 minutes, and 30 or 36 minutes are too slow.
Answer: (C) 48
Each word's code is the sum of its letters' alphabet positions: T + I + E = 20 + 9 + 5 = 34 and N + O + W = 14 + 15 + 23 = 52. So WAX = 23 + 1 + 24 = 48. 47, 46 and 45 are off by miscounting a letter.
Answer: (D) ₹ 1,200
Let x be lent at 5%; then 0·05x + 0·04(2000 − x) = 92, i.e. 80 + 0·01x = 92, so x = ₹ 1,200. Check: 60 + 32 = ₹ 92. ₹ 800 would give only ₹ 88 of interest.
Answer: (D) 0·5
With eight values the median is the mean of the 4th and 5th, (36 + 37) ÷ 2 = 36·5. After removing 35 there are seven values (30, 34, 36, 37, 38, 39, 40) and the median is the 4th, 37. The increase is 0·5, not 1 or more.
Answer: (A) 28 : 25
Take C = 100; then B = 80 and A = 80 × 1·4 = 112. So A : C = 112 : 100 = 28 : 25. Adding the percentages directly (40 − 20 = 20%) would wrongly suggest 6 : 5, and the other ratios do not fit.
Answer: (A) 37·5
Total for 28 students = 1400; the remaining 20 students average 55, totalling 1100. The 8 who left scored 1400 − 1100 = 300, an average of 300 ÷ 8 = 37·5. The other options would leave the new average different from 55.
Answer: (B) 4 hours
Call each of AB and BC one stretch. The round trip A→B→A is one stretch with the stream and one against it, taking 6 hours; A to C (two stretches) taking 8 hours means A→C is upstream at 4 hours a stretch. So one stretch downstream takes 6 − 4 = 2 hours, and C to A (two stretches downstream) takes 4 hours.
Answer: (A) 8 cm
The first square's area is $\frac{d^2}{2} = \frac{32}{2} = 16$ cm², so the second square's area is 32 cm². Its diagonal satisfies $\frac{d^2}{2} = 32$, so $d = 8$ cm. $8\sqrt{2}$ cm would correspond to doubling the diagonal (four times the area).
Answer: (A) 185
In each figure the bottom number is (sum of the top numbers) × (their difference): (11 + 5) × (11 − 5) = 96 and (15 + 9) × (15 − 9) = 144. So the missing number is (21 + 16) × (21 − 16) = 37 × 5 = 185. The other options do not follow this rule.
Answer: (A) 15
Let the numbers be 5x and 3x; then (5x + 3) : (3x + 3) = 14 : 9 gives 45x + 27 = 42x + 42, so x = 5. The numbers are 25 and 15, so the smaller is 15. 25 is the larger number, and 18 and 28 are those numbers after adding 3.
Answer: (D) ₹ 1,089
Here the loss is 10% of the selling price, i.e. 10% of ₹ 990 = ₹ 99. So the cost price is 990 + 99 = ₹ 1,089. ₹ 1,100 would be the answer if the loss were 10% of the cost price, which is the usual trap.
Answer: (A) 0
$x + \frac{1}{x} = -1$ gives $x^2 + x + 1 = 0$. Since $x^3 - 1 = (x - 1)(x^2 + x + 1)$, it equals 0. The values 1, −1 and 2 ignore this factorisation.
Answer: (C) 217800
Growth compounds yearly, so the population after 2 years is 180000 × 1·1 × 1·1 = 180000 × 1·21 = 217800. Adding a flat 20% would give 216000, which is not an option, and the other figures do not match $1.1^2$.
Answer: (C) $\frac{\pi}{3}^c$
The two angles add to 65°20′3″ + 54°39′57″ = 120°0′0″, so the third angle is 180° − 120° = 60°. In radians (circular measure) 60° is $\frac{\pi}{3}$. $\frac{2\pi}{3}$ is the sum of the two given angles, not the third one.
Answer: (B) 4 hours
A's speed is (12 + s) and B's is (15 − s) for stream speed s, so their closing speed is 27 km/hr whatever s is. They meet after 108 ÷ 27 = 4 hours. 4·5 and 6 hours would need a slower closing speed.
Answer: (A) 30 days
Together Ramesh and Rahman do $\frac{1}{20} + \frac{1}{25} = \frac{9}{100}$ of the work a day, so in 10 days they finish $\frac{90}{100}$. Suresh does the remaining $\frac{1}{10}$ in 3 days, so he alone needs 30 days. The other options do not match $\frac{1}{10}$ in 3 days.
Answer: (B) 75%
After the first discount the price is 50% of the original, and the second 50% leaves 25% of the original. The single equivalent discount is therefore 100 − 25 = 75%. Adding the two (100%) is the common mistake.
Answer: (C) ₹ 36
The question is meant as '4 eggs less are available for ₹ 24': a 50% price rise cuts what ₹ 24 buys by one-third, so those 4 eggs are one-third of the old quantity (12 eggs before, 8 eggs now). The present price is ₹ 24 ÷ 8 = ₹ 3 an egg, i.e. ₹ 36 a dozen. ₹ 24 was the old price per dozen, and ₹ 27 and ₹ 42 do not fit.
Answer: (C) 10%
Interest for the extra 2 years is 700 − 600 = ₹ 100, i.e. ₹ 50 a year, so the principal is 600 − 100 = ₹ 500. The rate is 50 ÷ 500 × 100 = 10%. Using ₹ 600 as the principal would give about 8·33%, which matches no option.
Answer: (C) 16 cm
Each chord of 12 cm is at a distance $\sqrt{10^2 - 6^2} = 8$ cm from the centre. Two distinct equal parallel chords lie on opposite sides of the centre, so they are 8 + 8 = 16 cm apart. 12, 14 and 18 cm do not come from this calculation.
Answer: (C) $-a, -b$
Move $\frac{1}{x}$ to the left: $\frac{1}{a + b + x} - \frac{1}{x} = \frac{a + b}{ab}$, which gives $\frac{-(a + b)}{x(a + b + x)} = \frac{a + b}{ab}$. So $x^2 + (a + b)x + ab = 0$, i.e. $(x + a)(x + b) = 0$ and $x = -a$ or $-b$. Positive $a$ or $b$ do not satisfy the equation.
Answer: (A) 800
Going from a 20% loss to a 5% profit is a swing of 25% of the cost price, and this equals ₹ 200. So the cost price is 200 ÷ 0·25 = ₹ 800. ₹ 8,000 would need a swing of ₹ 2,000.
Answer: (A) 16 years
To double, the simple interest must equal 100% of the principal. At 6·25% a year that takes 100 ÷ 6·25 = 16 years. 15 or 10 years would give only about 94% or 63% interest.
Answer: (C) ₹ 1,600; ₹ 2,400
Let incomes be 2x, 3x and expenses 5y, 9y; then 2x − 5y = 600 and 3x − 9y = 600. Solving gives y = 200 and x = 800, so the incomes are ₹ 1,600 and ₹ 2,400 (expenses ₹ 1,000 and ₹ 1,800). The other pairs are in ratio 2 : 3 but do not leave ₹ 600 savings each.
Answer: (A) $16 - \sqrt{3}$
Rationalising, $\frac{2 + \sqrt{3}}{2 - \sqrt{3}} = 7 + 4\sqrt{3}$ and $\frac{2 - \sqrt{3}}{2 + \sqrt{3}} = 7 - 4\sqrt{3}$, which add to 14. Also $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = \frac{4 - 2\sqrt{3}}{2} = 2 - \sqrt{3}$. The total is $16 - \sqrt{3}$; option C is only the last term.
Answer: (C) −20%
Take the salary as 100: after a 50% cut it is 50, and a 60% rise makes it 80. The net change is 80 − 100 = −20%. Simply adding −50 and +60 gives the wrong +10%.
Answer: (D) 8 days
A's daily work = $\frac{1}{6} - \frac{1}{12} = \frac{1}{12}$ and C's = $\frac{1}{6} - \frac{1}{8} = \frac{1}{24}$. Together A and C do $\frac{3}{24} = \frac{1}{8}$ a day, so they need 8 days. 6 days is the time for all three together.
Answer: (C) $16\frac{2}{3}$%
Take the selling price as 100; the loss is 20, so the cost price is 120. Loss on cost price = 20 ÷ 120 × 100 = $16\frac{2}{3}$%. 25% is what a 20% gain on selling price would be on cost, a different situation.
Answer: (C) 20
Total weight = 30 × 45 = 1350 kg. With b boys, 49b + 37(30 − b) = 1350, so 12b = 240 and b = 20. 10 is the number of girls, the most tempting wrong answer.
Answer: (C) 3
Writing everything as powers of 3, the left side is $\frac{3^{2n} \times 3^5 \times 3^9}{3^1 \times 3^{16}} = 3^{2n - 3}$. Setting $3^{2n - 3} = 3^3$ gives $2n = 6$, so $n = 3$. The other values give $3^{-3}$, $3^1$ or $3^5$.
Answer: (D) Uncle
The key's answer is (D) Uncle. An uncle does appear in the passage: C's father is A's uncle, and D's father is that uncle's brother. Note: D is one of the two daughters, so she cannot be an uncle; her father is an uncle of A, which makes D A's cousin, option (A), the same relation the key gives for C in Q61.
Answer: (B) 9·4 m
The ladder is the hypotenuse and the 4·7 m distance is adjacent to the 60° angle, so length = 4·7 ÷ $\cos 60^\circ$ = 4·7 ÷ $\frac{1}{2}$, i.e. the ladder is 9·4 m long. Option A, 4·7 m, is only the base distance.
Answer: (B) 55°
Where the external bisectors of B and C meet, $\angle BOC = 90^\circ - \frac{1}{2}\angle A$. With $\angle A = 70^\circ$ this is $90^\circ - 35^\circ = 55^\circ$. 125° would be the result for internal bisectors, and 45°, 65° and 75° do not fit the formula.
Answer: (C) ₹ 80,000
Last year's tax was 4% of ₹ 1,00,000 = ₹ 4,000. For the same tax at 5%, income = 4000 ÷ 0·05 = ₹ 80,000. ₹ 1,25,000 reverses the ratio and would raise the tax.
Answer: (B) 7 years
The son reaches the father's present age after (F − S) years, when both have aged by that amount: 36 + 2(F − S) = 80, so F − S = 22. With F + S = 36, the son is (36 − 22) ÷ 2 = 7 years old. The other ages do not give a 22-year gap.
Answer: (A) $9\frac{1}{11}$%
Reduction needed = $\frac{10}{100 + 10} \times 100 = \frac{100}{11} = 9\frac{1}{11}$%. A 10% cut is too much because it is measured on the old consumption. $11\frac{1}{9}$% is the extra consumption allowed when prices fall by 10%, a different case.
Answer: (B) 10 km North-East
Net movement is 15 − 9 = 6 km North and 8 km East. The straight-line distance is $\sqrt{6^2 + 8^2} = 10$ km, and he is north and east of the start, i.e. North-East. South-West reverses the direction.
Answer: (A) 112
Take the coins as 3x, 8x and 10x; their values are 3x, 4x and x rupees, totalling 8x = 112, so x = 14. The number of 50-paise coins is 8 × 14 = 112. 84 or 96 coins of 50 paise would not make the total value ₹ 112.
No option is correct as printed — this question is disputed. WBPSC awarded the mark to all candidates: no correct option — with sum 92 and ratio 2 : 3 : 4 the 1st number is 20 4/9, not any listed value (a sum of 90 would give 20).
The two ratios combine to 1st : 2nd : 3rd = 2 : 3 : 4, i.e. 9 parts, so the 1st number would be $\frac{2}{9} \times 92 = 20\frac{4}{9}$. That is not a whole number and matches none of the options; with a sum of 90 the answer would have been 20. The Commission therefore awarded the mark to all candidates.
Answer: (B) 9 kmph
Taking three times as long upstream means the downstream speed is three times the upstream speed: 18 + s = 3(18 − s). So 4s = 36 and s = 9 kmph. With s = 6 the downstream speed would be only twice the upstream speed.
Answer: (A) 76
He has 10 × 32 = 320 runs; an average of 36 over 11 innings needs 396 runs. So the next innings must bring 396 − 320 = 76 runs. Option C, 4, is only the rise wanted in the average, not the runs he must score.
Answer: (D) 70 kg
By alligation, the quantities at 7% and 17% are in the ratio (17 − 10) : (10 − 7) = 7 : 3. So 70 kg was sold at 7% profit and 30 kg at 17%. Option C (30 kg) is the part sold at 17%.
Answer: (A) 11 months
Profit is shared in the ratio of investment × time, so (11 × 8) : (12 × t) = 2 : 3. This gives 24t = 264, so t = 11 months. 8 months would make the profit ratio 11 : 12, the same as the investment ratio.
Answer: (C) 8
Rationalising each term gives $\frac{1}{\sqrt{n} + \sqrt{n + 1}} = \sqrt{n + 1} - \sqrt{n}$, so the sum telescopes. Everything cancels except $\sqrt{81} - \sqrt{1} = 9 - 1 = 8$. Option A forgets to subtract $\sqrt{1}$.
Answer: (C) ₹ 200
Payment is shared in proportion to the work done, and C did $1 - \frac{7}{11} = \frac{4}{11}$ of it. C's share is $\frac{4}{11} \times 550$ = ₹ 200. ₹ 350 is the combined share of A and B.
Answer: (B) 47
Here a = 5 and d = 7, so the 7th term is a + 6d = 5 + 42 = 47. 40 is the 6th term and 33 the 5th term.
Answer: (D) ₹ 720
Interest of ₹ 75 on ₹ 500 in 3 years means a rate of 75 ÷ (500 × 3) × 100 = 5%. On ₹ 600 for 4 years the interest is ₹ 120, so the amount is ₹ 720. ₹ 120 is only the interest, not the amount.
Answer: (D) Cousin
C is the only son of A's uncle, so C is A's cousin. F is E's sister and E is A's brother, so F is A's sister and C is F's cousin too. C is a child of the same generation, so 'uncle' and 'son' are impossible, and C's father is not F's father, so C is not her brother.
Answer: (C) 40% profit
With cost price 100, a 30% loss means a selling price of 70. Double that is 140, a profit of 40%. Doubling the 30% loss to 60% loss is the obvious trap.
Answer: (A) 40% loss
With a cost of 100, a 10% gain means a selling price of 110, and half of that is 55, so the sale ends in a heavy loss. Option (A) is the only large loss among the choices and is the answer in the key; it is exact if the original gain is 20%, since 120 ÷ 2 = 60. Worked with the printed 10%, the loss comes to 45%, which is not among the options, so the question appears to carry a misprint.
Answer: (D) 9·75
If $\frac{2}{3}$ of the number is 26, the number is 26 × $\frac{3}{2}$ = 39. 25% of 39 is 39 ÷ 4 = 9·75. The other decimals are near misses from rounding errors.
Answer: (D) 14 min 40 sec
In 4 minutes both pipes fill $4 \times (\frac{1}{15} + \frac{1}{20}) = \frac{7}{15}$ of the tank. B alone fills the remaining $\frac{8}{15}$ in $\frac{8}{15} \times 20 = 10\frac{2}{3}$ minutes, i.e. 10 min 40 sec. Total time = 4 min + 10 min 40 sec = 14 min 40 sec.
Answer: (D) 85 kg
An increase of 1 kg in the average of 25 persons means the total rose by 25 kg. So the new person weighs 60 + 25 = 85 kg. 61 kg adds only the 1 kg rise in the average.
Answer: (B) 3 : 4
To pass a pole the train covers its own length, 240 m; to cross the bridge it covers 240 + 80 = 320 m. At the same speed the times are in the ratio 240 : 320 = 3 : 4. Forgetting the train's own length on the bridge gives a wrong ratio such as 3 : 1.
Answer: (B) $33\frac{1}{3}$
SP of 60 − CP of 60 = SP of 15, so CP of 60 articles = SP of 45 articles. The gain is the SP of 15 on a cost equal to the SP of 45, i.e. 15 ÷ 45 = $33\frac{1}{3}$%. 25% wrongly divides by 60 instead of 45.
Answer: (C) 25%
Purchase price = 800 × 0·9 × 0·85 = ₹ 612, and with ₹ 28 transport the cost is ₹ 640. Selling at ₹ 800 gives a gain of ₹ 160, i.e. 160 ÷ 640 = 25%. Ignoring the transport cost would give about 30·7%.
Answer: (B) 1
Across the four views (i)–(iv), the face 2 is seen next to 6, 4, 3 and 5. A face cannot be adjacent to its opposite, so the only number left for the face opposite 2 is 1. 4, 5 and 3 are all seen beside 2.
Answer: (A) ₹ 28,938
Amount = 25000 × 1·04 × 1·05 × 1·06. Step by step: 26000, then 27300, then 28938. So the man receives ₹ 28,938; the other figures are off by small arithmetic slips.
Answer: (D) $9\frac{1}{11}$%
Selling 110 mangoes brings in what 120 cost, so on 110 mangoes the gain equals the cost of 10. Gain % = 10 ÷ 110 × 100 = $9\frac{1}{11}$%. 10% wrongly divides by 100, and $11\frac{1}{9}$% by 90.
Answer: (D) 8
By the remainder theorem the remainder is the value at $x = 1$: 1 + 3 + 3 + 1 = 8. Equivalently the polynomial is $(x + 1)^3$ and $2^3 = 8$. 0 would be the remainder on dividing by $(x + 1)$.
Answer: (C) ₹ 930
A = $\frac{2}{9}$(B + C) means A is $\frac{2}{11}$ of the total, ₹ 280; B = $\frac{3}{11}$(A + C) means B is $\frac{3}{14}$ of the total, ₹ 330. So C = 1540 − 280 − 330 = ₹ 930. ₹ 280 and ₹ 330 are A's and B's shares.
Answer: (A) ₹ 1,200
If 3A = 4B = 5C, the shares are in the ratio $\frac{1}{3} : \frac{1}{4} : \frac{1}{5}$ = 20 : 15 : 12, i.e. 47 parts. Each part is 2820 ÷ 47 = ₹ 60, so A gets 20 × 60 = ₹ 1,200 (B ₹ 900, C ₹ 720). ₹ 705 is a quarter of the total.
Answer: (C) 20
The mean proportional of a and b is $\sqrt{ab}$, so here it is $\sqrt{16 \times 25} = \sqrt{400} = 20$. 400 is the product itself, not its square root.
Answer: (B) ₹ 3
Simple interest for one year = ₹ 120. Compounded half-yearly at 5% per half-year, the amount is 1200 × 1·05 × 1·05 = ₹ 1,323, so the compound interest is ₹ 123. The difference is ₹ 3; it equals the interest on the first half-year's ₹ 60 interest (5% of 60).
Answer: (A) 45:56
Selling price = 0·9 × printed price = 1·12 × cost price. So cost : printed = 0·9 : 1·12 = 90 : 112 = 45 : 56. The other ratios do not satisfy this equation.
Answer: (B) ± 16
By the distance formula $(-12)^2 + y^2 = 20^2$, so $y^2 = 400 - 144 = 256$ and $y = \pm 16$. This is the 12-16-20 right triangle, so ± 15 and ± 14 do not fit.
Answer: (A) Figure (a)
Each figure is a triangle with three arrows. In (b), (c) and (d) two arrows point into the triangle and one points out of it, but in (a) only one arrow points in and two point out. So (a) is the odd figure.
Answer: (B) 2
Pair the factors: $(2 - \sqrt{3})(4 + 2\sqrt{3}) = 2(2 - \sqrt{3})(2 + \sqrt{3}) = 2(4 - 3) = 2$. Also $(\sqrt{5} + 2)(\sqrt{5} - 2) = 5 - 4 = 1$. The product is 2 × 1 = 2.
Answer: (C) Ice
An ocean is a huge mass of water, and a glacier is a huge mass of ice. Mountains are where glaciers are found and a refrigerator makes ice, but neither is what a glacier is made of.
Answer: (D) ₹ 4,000
Multiplying by 30, the capitals are 105 : 40 : 36. Over the year A's capital-months are 105 × 4 + 157·5 × 8 = 1680, B's 40 × 12 = 480 and C's 36 × 12 = 432, total 2592. B's share = $\frac{480}{2592} \times 21600$ = ₹ 4,000.
Answer: (C) 43
The group's total is 10 × 41 = 410; adding 63 makes 473 for 11 students. The new average is 473 ÷ 11 = 43. An average must rise when a higher score is added, so 39 and 40 are impossible.
Answer: (B) 19%
Area varies as $r^2$, so the new area is $0.9^2 = 0.81$ of the old one. The area falls by 19%. 20% simply doubles the 10% and ignores the $0.1^2$ term.
Answer: (C) $66\frac{2}{3}$%
Take B = 100; then A = 60. B exceeds A by 40, which as a percentage of A is 40 ÷ 60 × 100 = $66\frac{2}{3}$%. 40% wrongly measures the difference against B.
Answer: (C) 5·5%
Taking simple interest, the interest is $\frac{495}{2000}$ = 24·75% of the sum over 4·5 years. The yearly rate is 24·75 ÷ 4·5 = 5·5%. At 5% the interest would be only 22·5%.
Answer: (D) 27
Dividing by 4, $5^x = 125 = 5^3$, so $x = 3$. Then $x^x = 3^3 = 27$. 8 and 64 are $2^3$ and $4^3$, which use the wrong base.
Answer: (C) 400
The gap between 35% and 29% is 6% of the maximum, and it equals 24 marks. So the maximum is 24 ÷ 0·06 = 400. With 300 marks, 6% would be only 18.
Answer: (C) 10%
$\frac{6050}{5000} = 1.21 = (1.1)^2$, so $1 + \frac{r}{100} = 1.1$ and r = 10%. 5% would give an amount of only ₹ 5,512·50.
Answer: (A) 5
If the roots are reciprocals their product is 1. The product of roots is $\frac{k}{5}$, so $\frac{k}{5} = 1$ and $k = 5$. $k = 0$ would make one root zero, which has no reciprocal.
Answer: (B) 25%
The customer takes 4 items and pays for 3, so 1 of the 4 items' worth is free. The discount is 1 ÷ 4 = 25% of the total price. $33\frac{1}{3}$% wrongly divides the free item by the 3 paid items.
Answer: (D) 76
Out of 100 students, 60 are boys and 40 girls; 20% of 60 = 12 and 30% of 40 = 12 hold scholarships. So 24% get scholarships and 76% do not. 75% comes from simply averaging 20% and 30%.
Answer: (B) ₹ 340
Total parts = 4 × 9 + 5 × 8 + 6 × 4 = 36 + 40 + 24 = 100, so each part is ₹ 42·50. A woman gets 8 parts = ₹ 340. ₹ 1,700 is the share of all five women together.
Answer: (B) 3 years
Yearly interest = 4% of 2500 + 5% of 1800 = 100 + 90 = ₹ 190. Time = 570 ÷ 190 = 3 years. 2 or 4 years would give ₹ 380 or ₹ 760.
Answer: (A) 230 m
In opposite directions the relative speed is 200 km/h = $\frac{500}{9}$ m/s, so in 9 seconds they cover 500 m together. That is the sum of the two lengths, so the other train is 500 − 270 = 230 m.
Answer: (C) $h^2 + L^2$
For two numbers, $ab = hL$, and here $a + b = h + L$. So $a^2 + b^2 = (a + b)^2 - 2ab = (h + L)^2 - 2hL = h^2 + L^2$. Option B is $a + b$ itself, not the sum of squares.
Answer: (B) 3
The expression equals $\frac{1}{2}[(a - b)^2 + (b - c)^2 + (c - a)^2]$. Here that is $\frac{1}{2}(1 + 1 + 4) = 3$. It would be 0 only if $a = b = c$.
Answer: (C) 550
The sum is $10 \times (1 + 2 + \cdots + 10) = 10 \times 55 = 550$. 450 stops at $i = 9$, and 650 adds an extra 100.
Answer: (B) 6 cm
With D on BC, triangles BAD and BCA share angle B and have ∠BAD = ∠BCA, so they are similar. Hence $\frac{BD}{BA} = \frac{AD}{CA} = \frac{3}{8}$, giving BD = 16 × $\frac{3}{8}$ = 6 cm. 3 cm just repeats AD.
Answer: (B) 6 days
Together they do $\frac{1}{12} + \frac{1}{15} = \frac{3}{20}$ a day, so in 4 days they finish $\frac{3}{5}$ of the work. B alone does the remaining $\frac{2}{5}$ in $\frac{2}{5} \times 15 = 6$ days. 10 days would be B's time for $\frac{2}{3}$ of the work.
Answer: (C) $9\frac{1}{11}$%
100 units of water become 110 units of ice; on melting, 110 falls back to 100. The decrease is 10 out of 110, i.e. $\frac{100}{11} = 9\frac{1}{11}$%. 10% or more would measure the change against the water volume instead of the ice.
Answer: (B) 4 : 3
For two trains starting together towards each other, speed ratio = $\sqrt{t_2} : \sqrt{t_1}$, where $t_1$, $t_2$ are their times after meeting. Here that is $\sqrt{16} : \sqrt{9}$ = 4 : 3. 9 : 16 is the ratio of the times, not of the speeds.
Answer: (D) 3 hours 45 minutes
One tap fills the first half in 3 hours. Four taps together fill $\frac{4}{6}$ of the tank per hour, so the second half takes $\frac{1}{2} \div \frac{2}{3} = \frac{3}{4}$ hour = 45 minutes. Total = 3 hours 45 minutes.
Answer: (A) ₹ 51·25
SI of ₹ 50 for 2 years at 5% means the principal is ₹ 500. CI = 500 × (1·05² − 1) = 500 × 0·1025 = ₹ 51·25. The extra ₹ 1·25 is interest on the first year's ₹ 25 interest.
Answer: (C) ₹ 18·40
Total cost = 2 × 15 + 3 × 13 = ₹ 69 for 5 kg, i.e. ₹ 13·80 per kg. Adding $\frac{1}{3}$ of it as profit gives 13·80 × $\frac{4}{3}$ = ₹ 18·40 per kg. ₹ 17·40 would be a profit of only about 26%.
Answer: (A) ₹ 30
Paying ₹ 21 after a 30% discount means ₹ 21 is 70% of the marked price. Marked price = 21 ÷ 0·7 = ₹ 30. Adding 30% to ₹ 21 would give about ₹ 27·30, which is the usual mistake.
Answer: (D) 41 : 15
Taking one unit of each, milk = $\frac{5}{7} + \frac{3}{4} = \frac{41}{28}$ and water = $\frac{2}{7} + \frac{1}{4} = \frac{15}{28}$. So the new ratio is 41 : 15. 8 : 3 wrongly adds the ratio terms directly.
Answer: (A) 12 km/hr
For equal distances the average speed is $\frac{2xy}{x + y} = \frac{2 \times 10 \times 15}{25} = 12$ km/hr. 12·5 km/hr is the simple mean of the speeds, which is wrong because more time is spent at the slower speed.
Answer: (A) −1
$4^{x+2} = 2^{2x+4} = 2 \times 2^{2x+3}$, so the equation becomes $2^{2x+3} = 2$. Hence $2x + 3 = 1$ and $x = -1$. Check: $4^1 = 4 = 2^1 + 2$.
Answer: (B) $11\frac{1}{9}$%
He gives 900 g but charges for 1000 g, gaining 100 g on every 900 g he actually sells. Profit % = 100 ÷ 900 × 100 = $11\frac{1}{9}$%. 10% wrongly divides by 1000 g.
Answer: (A) 17
Doctors who are neither players nor artists lie in the part of the triangle outside both the circle and the rectangle, which holds 17. The 8 are doctors who are artists, and 4 and 3 are doctors who are players.
Answer: (C) ₹ 34·50
The ratio has 2 + 5 + 4 = 11 parts, so one part = 126·50 ÷ 11 = ₹ 11·50. B exceeds A by 5 − 2 = 3 parts = ₹ 34·50. The other options are off by a rupee or two.
Answer: (C) 72
The terms are $2n^2$: 2 × 1, 2 × 4, 2 × 9, 2 × 16, 2 × 25, so the next is 2 × 36 = 72. The differences 6, 10, 14, 18 also grow by 4, giving 50 + 22 = 72.
No option is correct as printed — this question is disputed. WBPSC awarded the mark to all candidates: no correct option — the journey works out to 70 km, which is not listed (140 km would need a 30-minute delay).
The extra time is $\frac{d}{35} - \frac{d}{40} = \frac{d}{280}$ hours, and setting this to $\frac{1}{4}$ hour gives d = 70 km. 70 km is not among the options; 140 km would make the train 30 minutes late. The Commission therefore awarded the mark to all candidates.
Answer: (C) 53
Persons who know all three languages are in the central region common to the three circles, which shows 53. 65, 62 and 47 are the regions common to only two languages (Hindi–Bengali, Bengali–English and Hindi–English).
Answer: (B) ₹ 250
₹ 266 is 95% of the labelled price, so the labelled price is ₹ 280. Selling at ₹ 280 gives a 12% profit, so the cost price is 280 ÷ 1·12 = ₹ 250. ₹ 280 is the labelled price, not the cost.
Answer: (C) 25
Artists who are players are in the overlap of the rectangle and the circle: 22 (not doctors) plus 3 (also doctors) = 25. 29 and 30 wrongly add the 4 or 8 regions, which lie outside that overlap.
Answer: (B) 10 days
Adding the three pairs counts each person twice: $2(A + B + C) = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{1}{5}$. So A + B + C = $\frac{1}{10}$ per day, i.e. 10 days. 5 days forgets to halve the sum.
Answer: (D) ₹ 250
3H = 5C means a cow costs $\frac{3}{5}$ of a horse. Then 4H + 6 × $\frac{3}{5}$H = 7·6H = 1900, so H = ₹ 250 (and a cow ₹ 150). ₹ 150 is the cost of a cow.
Answer: (C) ₹ 500
Profit percentage is measured on cost price, so the extra ₹ 35 equals 7% of the cost price. Cost price = 35 ÷ 0·07 = ₹ 500. ₹ 245 multiplies instead of dividing.
Answer: (C) $22\frac{2}{5}$ cm
11 litres = 11000 cm³ and the base area is $\frac{22}{7} \times 12.5^2 = \frac{6875}{14}$ cm². The drop is $11000 \times \frac{14}{6875} = 22.4$ cm = $22\frac{2}{5}$ cm. Using the diameter instead of the radius would give a much smaller drop.
Answer: (A) 5% profit
On a cost of 100: half (50) gains 10, a quarter (25) loses 5 and the last quarter (25) breaks even. Net gain = 10 − 5 = 5 on 100, a 5% profit. 'Neither loss nor gain' wrongly treats the 20% profit and 20% loss as cancelling, though they apply to different quantities.
Answer: (A) 60 cc
The mixture has 60 cc water and 180 cc glycerine. For water : glycerine = 2 : 3 the water must be 120 cc, so 120 − 60 = 60 cc must be added. 80 cc would make the ratio 7 : 9.
Answer: (C) 15 days
B does 1·4 times A's daily work, so B needs 21 ÷ 1·4 = 15 days. Cutting 40% off A's time gives about 12·6 days, which is the usual trap.
Answer: (B) 40
The total work gives 8(4m + 6w) = 10(3m + 7w), so 32m + 48w = 30m + 70w and one man equals 11 women. Then 4 men + 6 women = 50 women, who take 8 days, so the work is 400 woman-days. 10 women need 400 ÷ 10 = 40 days.
Answer: (C) 9
In each figure the centre = (left + right) − (top + bottom): (13 + 15) − (9 + 12) = 7 and (16 + 14) − (8 + 13) = 9. For the third figure, (15 + 17) − (9 + 14) = 32 − 23 = 9. The other options do not follow this rule.
Answer: (B) 16 litres
By alligation, first : second = (17 − 13) : (25 − 17) = 4 : 8 = 1 : 2. So with 8 litres of the first, 16 litres of the second are needed. 4 litres reverses the ratio.
Answer: (D) 800 grams
He charges for 1000 g but gives w g, and his gain is (1000 − w) ÷ w = 25%. So 1000 = 1·25w and w = 800 g. 750 g would give a gain of $33\frac{1}{3}$%.
Answer: (A) ₹ 625
After the deductions the total is 1570 − 25 − 45 = ₹ 1,500, shared 2 : 3 as ₹ 600 and ₹ 900. Adding back the deductions, A received 600 + 25 = ₹ 625 (and B ₹ 945). ₹ 945 is B's amount.
Answer: (A) $6\frac{1}{4}$%
At simple interest, doubling means interest equal to 100% of the sum. Over 16 years that is 100 ÷ 16 = 6·25% a year, i.e. $6\frac{1}{4}$%. 6% would take about $16\frac{2}{3}$ years.
Answer: (B) 4 : 6 : 3
Capital × time: A = 2 × 12 = 24, B = 3 × 12 = 36, C = 3 × 6 = 18. So the profit ratio is 24 : 36 : 18 = 4 : 6 : 3. 2 : 3 : 3 ignores that C was in for only 6 months.
Answer: (A) 50 km
In the same time, the faster speed covers 4 km more each hour, so 20 km extra takes 5 hours. The actual distance at 10 km/hr is 10 × 5 = 50 km. 70 km is the distance at the faster speed.
Answer: (D) ₹ 5,000
Each person spends 4500 ÷ (15 × 6) = ₹ 50 a month. For 25 persons over 4 months the total is 25 × 4 × 50 = ₹ 5,000. The smaller amounts treat the expenditure as falling with more people.
Answer: (D) 6 cm
The increase is $4\pi[(r + 2)^2 - r^2] = 16\pi(r + 1) = 352$. With $\pi = \frac{22}{7}$, $r + 1 = 352 \times \frac{7}{352} = 7$, so $r = 6$ cm. A radius of 5 cm would give an increase of only about 302 cm².
Answer: (A) 3
Add the letters' alphabet positions and reduce to a single digit: P + S + T = 16 + 19 + 20 = 55, then 5 + 5 = 10 and 1 + 0 = 1. Likewise N + P + R = 14 + 16 + 18 = 48, then 4 + 8 = 12 and 1 + 2 = 3. So the answer is 3.
Answer: (D) 14 years
Four years ago the sum was 72 − 12 = 60, shared 1 : 2 : 3 as 10, 20 and 30. A's present age is 10 + 4 = 14 years. 12 years wrongly divides the present total of 72 in the ratio.
Answer: (C) 135
Each inner triangle is the product of its own outer number and the next outer number clockwise: top 7 × 9 = 63, bottom 15 × 2 = 30 and left 2 × 7 = 14. So the right triangle is 9 × 15 = 135. 18 and 33 do not fit this rule.
Answer: (A) 4% decreased
100 becomes 120 and then 120 × 0·8 = 96. The salary falls by 4%. It does not remain the same because the 20% cut is taken on the larger figure.
Answer: (C) 15 years
Doubling in 5 years means interest of 100% in 5 years, i.e. 20% a year. Becoming four times needs 300% interest, which takes 15 years. 10 years would be right only for compound growth.
Answer: (A) 30 days
A's rate = $\frac{1}{2} \div \frac{3}{4} = \frac{2}{3}$ of B's rate. Together they work at $\frac{5}{3}$ of B's rate, which equals $\frac{1}{18}$ per day, so B alone does $\frac{1}{30}$ per day. B needs 30 days; 45 days is A's time.
Answer: (C) 52 cm
The diagonals of a rhombus bisect each other at right angles, so each side is $\sqrt{12^2 + 5^2} = 13$ cm. The perimeter is 4 × 13 = 52 cm. 13 cm is just one side.
Answer: (C) 24 kg
The salt stays the same: 0·15x = 0·18(x − 4). So 0·03x = 0·72 and x = 24 kg. Check: 3·6 kg of salt is 15% of 24 kg and 18% of 20 kg.
Answer: (B) 3,200
Principal = 3528 ÷ $1.05^2$ = 3528 ÷ 1·1025 = 3,200. Check: 3200 → 3360 → 3528. 3,000 would grow only to 3,307·50.
Answer: (B) 57463822
With boys : girls = 7 : 4, the total must be a multiple of 11. Using the alternating-digit test, 29435417, 28444625 and 29434526 each give 11, so they are divisible by 11. 57463822 gives 9, so it is not a multiple of 11 and cannot be the total.
Answer: (C) ₹ 12,100
Half-yearly compounding at 20% p.a. means 10% for each of 2 half-years. Amount = 10000 × 1·1 × 1·1 = ₹ 12,100. ₹ 12,000 is the simple-interest amount, and ₹ 14,400 compounds 20% twice.
Answer: (A) 72 km/hr
The extra 60 m of bridge takes 3 extra seconds, so the speed is 20 m/s. 20 m/s × $\frac{18}{5}$ = 72 km/hr (the train is 120 m long). The other speeds do not fit both timings.
Answer: (D) 24 minutes
In 30 minutes A fills $\frac{30}{60} = \frac{1}{2}$ of the cistern, so B must fill the other half. B fills half in $\frac{48}{2} = 24$ minutes, so B is turned off after 24 minutes.
Answer: (B) Figure (b)
In (a), (c) and (d) a simple shape (a square, a circle, a triangle) is divided into four parts by two crossing lines drawn inside it. Figure (b) is instead a plus-shaped outline made of five small squares, so it is the odd one.
Answer: (B) 6
The expression $\frac{x^2}{x}$ is not defined at $x = 0$, so 0 cannot be a root. For $x \ne 0$ it equals $x$, so $x = 6$. Option C wrongly keeps the root 0 that appears after multiplying through by $x$.
Answer: (A) 14 years
After t years, 50 + t = 2(18 + t), so 50 + t = 36 + 2t and t = 14. Check: A will be 64 and B 32. 16 years would make them 66 and 34.
Answer: (A) $\sqrt{3} : 1$
Equal volumes give $r_1^2 h_1 = r_2^2 h_2$, so $\frac{r_1^2}{r_2^2} = \frac{h_2}{h_1} = 3$. Hence $r_1 : r_2 = \sqrt{3} : 1$; the shorter cylinder must be wider. Option B reverses the ratio, and 3 : 1 forgets the square root.
Answer: (C) 16800
Valid votes = 98% of 75% of the voters, and the winner has 75% of these, so 0·75 × 0·98 × 0·75 × V = 9261. That is 0·55125V = 9261, giving V = 16800. 1680 and 168000 are off by a factor of ten.
Answer: (B) ₹ 17,600
Let the 6th man give x; then x = $\frac{100000 + x}{6}$ − 2000. So 6x = 100000 + x − 12000, 5x = 88000 and x = ₹ 17,600. Check: the average is 117600 ÷ 6 = ₹ 19,600, which is ₹ 2,000 more than x; ₹ 19,600 is the average, not his share.
Answer: (A) 14 cm
Foil area = 57·75 ÷ 0·10 = 577·5 cm², which is the curved surface $\pi r l$ with r = 10·5 cm, so $l = 577.5 \div 33 = 17.5$ cm. Height = $\sqrt{17.5^2 - 10.5^2} = \sqrt{196} = 14$ cm. 28 cm and 7 cm are double and half of this.
Answer: (D) 5 km/hr
Downstream speed = 24 ÷ 4 = 6 km/hr and upstream speed = 24 ÷ 6 = 4 km/hr. The boat's speed in still water is their average, (6 + 4) ÷ 2 = 5 km/hr. 6 km/hr is the downstream speed.
Answer: (C) 1411
6·5a = 8·5b gives a : b = 8·5 : 6·5 = 17 : 13. The greater number is $\frac{17}{30} \times 2490 = 1411$, and the smaller is 1079. Option A is the smaller number.
Answer: (A) 5%
After the first 20% discount the price is 1050 × 0·8 = ₹ 840. The second discount takes it from ₹ 840 to ₹ 798, a cut of ₹ 42, which is 42 ÷ 840 = 5%. A 6% or larger second discount would take the price below ₹ 798.
Answer: (B) 2800
With S sweets, $\frac{S}{140} - \frac{S}{175} = 4$, i.e. $\frac{35S}{24500} = 4$, so S = 2800. Check: 2800 ÷ 175 = 16 and 2800 ÷ 140 = 20, which is 4 more. 2400 does not divide evenly by 175.
Answer: (C) 16%
On a cost of 100 the marked price is 120, and a 30% discount brings it to 84. The loss is 16 on 100, i.e. 16%. 10% wrongly subtracts the percentages directly.
No option is correct as printed — this question is disputed. WBPSC awarded the mark to all candidates: no correct option — the rate difference works out to 0·25%, not 25%.
With simple interest, 500 × 2 × d ÷ 100 = 2·5 gives a rate difference of d = 0·25%. None of the options shows 0·25%; option A's 25% appears to be that figure with the decimal point lost. The Commission therefore awarded the mark to all candidates.
Answer: (C) 4% decrease
Sales value = price × number = 0·8 × 1·2 = 0·96 of the original. So total sales fall by 4%. 'No effect' wrongly assumes the −20% and +20% cancel out.
Answer: (B) 60 minutes
At $\frac{5}{4}$ of the speed the time is $\frac{4}{5}$ of the usual time, a saving of $\frac{1}{5}$ of it. So $\frac{1}{5}$ of the usual time = 12 minutes, and the usual time is 60 minutes. 48 minutes is the time at the faster speed.
Answer: (A) 1
Substituting gives 7 + 24 ÷ 8 − 6 ÷ 2 × 3. Doing division and multiplication first: 24 ÷ 8 = 3 and 6 ÷ 2 × 3 = 9, so the value is 7 + 3 − 9 = 1. Working strictly left to right without BODMAS gives a different, wrong value.
Answer: (D) ₹ 400
B should get $\frac{5}{8}$ of the amount but gets $\frac{3}{5}$; the difference is $\frac{25 - 24}{40} = \frac{1}{40}$ of the amount. So $\frac{1}{40}$ of the amount = ₹ 10 and the amount is ₹ 400. Check: B gets ₹ 240 instead of ₹ 250.
Answer: (C) 900 liters
For capacity C, A fills $\frac{C}{15}$ litres a minute and together they fill $\frac{C}{45}$ a minute. So $\frac{C}{15} - 40 = \frac{C}{45}$, giving $\frac{2C}{45} = 40$ and C = 900 litres. Check: A gives 60 litres a minute, net 20, and 900 ÷ 20 = 45 minutes.
Answer: (C) 24 days
Together Bulu and Tathagata do $\frac{1}{20} + \frac{1}{30} = \frac{1}{12}$ a day, so in 7 days they finish $\frac{7}{12}$. Anita does the remaining $\frac{5}{12}$ in 10 days, so the whole work takes her $10 \times \frac{12}{5} = 24$ days.
Answer: (C) 3·5 km/hr
Downstream speed = 15 ÷ 3 = 5 km/hr and upstream speed = 15 ÷ 7·5 = 2 km/hr. Speed in still water = (5 + 2) ÷ 2 = 3·5 km/hr. 1·5 km/hr is the speed of the stream.
Answer: (B) 4 years
₹ 1,500 at 10% for 12 years earns 1500 × 10 × 12 ÷ 100 = ₹ 1,800. ₹ 2,500 at 18% earns ₹ 450 a year, so it needs 1800 ÷ 450 = 4 years. 3 years would give only ₹ 1,350.
Answer: (A) 6 months
A put in 1 part and B 3 parts of the capital, and A's profit share of $\frac{1}{3}$ means A : B = 1 : 2. So (1 × 9) : (3 × t) = 1 : 2, giving 3t = 18 and t = 6 months. 12 months would give A only $\frac{1}{5}$ of the profit.
Answer: (D) 3
The four numbers in each circle add up to 100: 14 + 36 + 25 + 25 = 100 and 20 + 50 + 20 + 10 = 100. In the third circle 36 + 54 + 7 = 97, so the missing number is 3. The other options give totals of 97 to 99.
Answer: (B) ₹ 7
SI of ₹ 350 for 2 years at 4% means the principal is 350 ÷ 0·08 = ₹ 4,375. For 2 years, CI − SI = P × $(\frac{r}{100})^2$ = 4375 × 0·0016 = ₹ 7. ₹ 3.50 is only half of this extra interest.
Answer: (D) 55
From a + 4d = 41 and a + 10d = 20, 6d = −21 so d = −3·5. Then a = 41 − 4 × (−3·5) = 41 + 14 = 55. 45 and 35 come from using the wrong number of steps or the wrong sign of d.
Answer: (A) 5000
83% passed in at least one subject, so those who passed both = 58 + 68 − 83 = 43%. If 43% is 2150 candidates, the total is 2150 ÷ 0·43 = 5000. 6000 would make 43% equal 2580.
Answer: (B) 0
The constants are $k_1 = z(x - y)$, $k_2 = x(y - z)$ and $k_3 = y(z - x)$. Adding, $zx - zy + xy - xz + yz - yx = 0$. So the sum is 0, not ±1.
Answer: (A) ₹ 8,100
Depreciation compounds on the reduced value each year, so the worth after 2 years is 14400 × 0·75 × 0·75 = ₹ 8,100. The value after only one year would be ₹ 10,800, and a flat 50% cut would give ₹ 7,200.
Answer: (D) ₹ 700
4% for 6 years is 24% of the sum and 5% for 4 years is 20%, a difference of 4%. So 4% of the sum = ₹ 28 and the sum is ₹ 700. ₹ 400 or ₹ 500 would give a difference of only ₹ 16 or ₹ 20.
Answer: (C) $\frac{9}{4}$ cm
The sphere displaces $\frac{4}{3}\pi \times 3^3 = 36\pi$ cm³ of water. Spread over the base $\pi \times 4^2 = 16\pi$ cm², the rise is $\frac{36}{16} = \frac{9}{4}$ cm. Option B inverts this fraction.
Answer: (C) ₹ 4,720
A's capital-months = 17000 × 4 + 21000 × 8 = 236000 and B's = 20000 × 12 = 240000, so the ratio is 59 : 60. A's share = $\frac{59}{119} \times 9520$ = ₹ 4,720. ₹ 4,800 is B's share.
Answer: (D) ₹ 6,600
The bill is wage × number, so it changes in the ratio (22 × 3) : (25 × 2) = 66 : 50. Original bill = 5000 × $\frac{66}{50}$ = ₹ 6,600. The other figures do not fit this 66 : 50 change.
Answer: (B) 24
People who had at least one type = 60 + 30 − 15 = 75%, so 25% had neither. 25% of 96 = 24. Forgetting to subtract the 15% overlap would wrongly give 10%.
Answer: (B) 1707
Each term is 4 times the previous one minus 1: 2 × 4 − 1 = 7, 7 × 4 − 1 = 27, 27 × 4 − 1 = 107 and 107 × 4 − 1 = 427. So the next term is 427 × 4 − 1 = 1707. The other options do not follow this rule.
Answer: (B) 6·67%
Turnover = price × quantity, so quantity = 1·12 ÷ 1·20 = 0·9333 of the original. The decrease is $6\frac{2}{3}$%, which rounds to 6·67%. 6·66% cuts off the recurring 6 instead of rounding it, and 5% and 5·67% are too small.
Answer: (D) KEQI
Each letter moves 4 places forward: P → T, L → P, A → E, Y → C (wrapping past Z). So G → K, A → E, M → Q, E → I, giving KEQI. KEQA wrongly shifts the last letter backwards.
Answer: (B) 200%
With the radius fixed, the cone's volume $\frac{1}{3}\pi r^2 h$ is proportional to its height. Making the height three times the original makes the volume three times too, an increase of 200%. 300% confuses 'three times' with 'an increase of three times'.
Answer: (C) 20 ft
Pool plus wall has area $\frac{36}{25}$ of the pool, so the outer radius is $\frac{6}{5}$ of the pool radius R. Then R + 4 = $\frac{6R}{5}$, giving R = 20 ft. With R = 16 ft the wall's share would be about 0·56 of the pool.
Answer: (D) 2
$\frac{2420}{2000} = 1.21 = 1.1^2$, so the time is 2 years. Check: 2000 → 2200 → 2420. 3 years would give ₹ 2,662.
Answer: (D) XW
Each letter is replaced by its opposite in the alphabet: A ↔ Z and B ↔ Y, so AB : ZY. In the same way C ↔ X and D ↔ W, so CD : XW. WX has the right letters in the wrong order.
Answer: (A) 50 km
In the same time the faster pace covers 4 km more per hour, so the 20 km extra means 5 hours of walking. At the actual speed of 10 km/hr he covered 50 km. 70 km is what he would have covered at 14 km/hr.
Answer: (D) X gains ₹ 3,150
X sells to Y for 150000 × 1·05 = ₹ 1,57,500 and buys it back for 157500 × 0·98 = ₹ 1,54,350. X ends up with the house again and ₹ 1,57,500 − ₹ 1,54,350 = ₹ 3,150 more, so X gains ₹ 3,150. ₹ 4,350 is the difference between the buy-back price and the original worth.
Answer: (D) 28th
Rank from the last = total − rank from the top + 1 = 35 − 8 + 1 = 28th. 27th forgets to add 1, since the student is counted in both rankings.
Answer: (D) 760
The rule is next term = term × n + $n^2$ for n = 1, 2, 3…: 1 × 1 + 1 = 2, 2 × 2 + 4 = 8, 8 × 3 + 9 = 33, 33 × 4 + 16 = 148. The next term should be 148 × 5 + 25 = 765, and 765 × 6 + 36 = 4626 confirms it, so 760 is wrong. 8, 33 and 148 all fit the rule.
Answer: (A) Monday
2000 is a leap year (divisible by 400), so it has 366 days = 52 weeks + 2 odd days. The day moves forward two places from Saturday, to Monday. Sunday would be the answer for a 365-day year.
Answer: (B) 15 days
In each 3-day cycle P does $\frac{3}{20}$ and Q and R together add $\frac{1}{30} + \frac{1}{60} = \frac{1}{20}$ on the third day, a total of $\frac{1}{5}$. Five such cycles finish the job, which is 15 days. 16 or 17 days overshoot the exact finish.
Answer: (D) $8\frac{1}{4}$ minutes
In 3 minutes both pipes fill $3 \times (\frac{1}{12} + \frac{1}{15}) = \frac{9}{20}$ of the cistern. Q alone fills the remaining $\frac{11}{20}$ in $\frac{11}{20} \times 15 = 8\frac{1}{4}$ minutes. The other fractions come from slips in this arithmetic.
Answer: (C) $133\frac{1}{3}$
The alloy has 125 g zinc and 75 g copper. For zinc : copper = 3 : 5 the copper must be 125 × $\frac{5}{3}$ = $208\frac{1}{3}$ g, so $133\frac{1}{3}$ g must be added. Only copper changes, so the zinc stays at 125 g.
Answer: (D) ₹ 15,000
The two loans differ by 2 years at 12%, i.e. 24% of each amount, and this is ₹ 1,800. So each amount is ₹ 7,500 and the total lent is ₹ 15,000. ₹ 7,500 is only one of the two equal amounts.
Answer: (B) 386
Each term is the previous one divided by 4: 24576 ÷ 4 = 6144, 6144 ÷ 4 = 1536, and 1536 ÷ 4 = 384, not 386. Then 384 ÷ 4 = 96 and 96 ÷ 4 = 24 fit, so 386 is the odd number.
Answer: (B) 40
Two series alternate: 10, 13, 16, 19 (adding 3) and 5, 10, 20, ? (doubling). The missing term belongs to the second series, so it is 20 × 2 = 40. 22 would be the next term of the first series.
Answer: (C) $\frac{1001}{3}$
Each factor simplifies: $2 - \frac{1}{3} = \frac{5}{3}$, $2 - \frac{3}{5} = \frac{7}{5}$, …, $2 - \frac{997}{999} = \frac{1001}{999}$. In the product $\frac{5}{3} \times \frac{7}{5} \times \cdots \times \frac{1001}{999}$ every numerator cancels the next denominator, leaving $\frac{1001}{3}$. Option B is just the last factor.
