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WBCS Preliminary Examination 2023 — General Studies · Question 122 of 200

Q122
ArithmeticAverages & Ages
In a cricket match, 5 batsmen A, B, C, D, E scored an average of 35 runs. D scored 5 more than E, E scored 20 fewer than A. B scored as many as D and E combined. B and C scored 75 between them. How many runs did C score?
  1. a.45
  2. b.55
  3. c.20
  4. d.30

Answer: (C) 20

Total runs $=5\times35=175$. Let E's score be $e$. Then $D=e+5$, $A=e+20$ (E scored 20 fewer than A) and $B=D+E=2e+5$. Since $B+C=75$, the total is $A+(B+C)+D+E=(e+20)+75+(e+5)+e=3e+100=175$, so $e=25$. Hence $D=30$, $A=45$, $B=55$ and $C=75-55=20$. Check: $45+55+20+30+25=175$. Options (A) 45, (B) 55 and (D) 30 are the scores of A, B and D, so make sure you answer for the batsman actually asked.

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