In a Cricket match, 5 batsmen A, B, C, D and E scored an average of 36 runs. If D scored 5 more than E, E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them, then [[1]] runs did E score.

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Detailed Solution

Concept- E scores 20 runs.
First, we will calculate the sum of the runs scored by A, B, C, D and E from the formula of mean or average which is
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Also, let us assume the runs scored by A to be

. Then, we will calculate the individual runs scored by the other four players in terms of

based on the conditions mentioned in theQuestion statement. Then, we will form a linear equation of single variable

by equation the summation of the individual runs scored by each player and the summation of their runs calculated from the formula of mean. Solving this equation for

, we will obtain our desired answer.
Given, 5 batsmen A, B, C, D and E scored an average of 36 runs, i.e.,
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Now, since assumed, that A scored

runs, given in theQuestion is that, E scored 8 fewer than A, i.e.,

D scored 5 more than E, i.e.,

.
B scored as many as D and E combined, i.e.,
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And B and C scored 107 between them. Let us assume C scored “c” runs, Therefore,
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Therefore, summation of the runs scored by all 5 batsmen are
Question Image

Hence, the correct answer is 20.

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