Discussion
In a cricket match, five batsmen A, B, C, D and E scored an average of 41 runs. D scored 5 more than E; E scored 8 fewer than A; B scored 5 fewer than D and E combined; B and C scored 117 between them. How many runs did C score ?
Answer: C
C scored 67 runs.
The total is 5 × 41 = 205. Express everything in terms of E: D = E + 5, A = E + 8, and B = D + E - 5 = 2E. Since B + C = 117:
\[ \begin{aligned} A + D + E + (B + C) &= 205 \\ (E + 8) + (E + 5) + E + 117 &= 205 \\ 3E &= 75 \Rightarrow E = 25 \end{aligned} \]
So B = 50 and C = 117 - 50 = 67. Check: A = 33, D = 30, E = 25, B = 50, C = 67, total 205. 37, 85 and 53 do not satisfy all the conditions together.
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