CAT 2020 Slot 3 QA Question 26: 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

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

Accepted Answer

The sum of the first $n$ innings is $30n$.

$\dfrac{30n + 38 + 15}{n+2} = 29$

$\Rightarrow 30n + 53 = 29n + 58$
$\Rightarrow n = 5$

Sum of first 5 innings = $30 	imes 5 = 150$

To make the lowest score as small as possible, make the other four scores as large as possible. Each of them must be les