cat 2020 Question 17

Question

A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first n innings. In these n innings, his average score was 30 runs and lowest score was x runs. The smallest possible value of x is

Accepted Answer

Given, $\frac{ ext{sum of scores in n matches} + 38 + 15}{n+2} = 29$

Given, $\frac{ ext{sum of scores in n matches}}{n} = 30$

30n + 53 = 29(n+2) $\Rightarrow n = 5$

Sum of the scores in 5 matches = $29 \cdot 7 - 38 - 15 = 150$

Since the batsmen scored less than 38 in each of the first 5 innings,

the value of x will be minimum when the remaining four values are highest

$\Rightarrow$ 37 + 37 + 37 + 37 + x = 150

$\Rightarrow$ x = 2

Question 17.

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Question 17.

Question Explanation

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