Simple & Compound Interest: previous-year questions

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: (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: (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) 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: (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: (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: (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: (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: (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: (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: (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) ₹ 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: (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: (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: (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: (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.

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: (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: (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: (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.