# A batsman in his 16 th innings makes a score of 70 and thereby increases his average

by 2 runs. If he had never been 'not out', then his average after 16 th innings is:

(a) 36

(b) 38

(c) 40

(d) 42

(e) 44

Answer

Verified

326.7k+ views

Hint: Let his average after 15 innings be x runs. So, his total score after 15 innings will

become 15x. Now, after the 16 th innings, total runs become 15x + 70 and new average

becomes x + 2. Put these in the average formula to solve for x and then find x + 2 which is

the answer.

Complete step by step solution:

We are given that a batsman makes a score of 70 in his 16 th innings. This score increases his

average by 2 runs.

We need to find his average after the 16 th innings.

Let his average after 15 innings be x runs.

So, applying the formula for average:

\[x=\dfrac{Total Score Upto 15 Innings}{15}\]

Total score after 15 innings = 15x

Now, in his 16 th innings, he scores 70 runs and his average increases by 2 runs.

So, his new average = x+2

His total score after 16 innings = 15x + 70

We can show this by:

\[x+2=\dfrac{15x+70}{16}\]

\[16x+32=15x+70\]

\[x=38\]

So, his average after the first 15 innings was 38 runs.

Now, we are given in the question that after the 16 th innings, his average increases by 2 runs

So, his new average after 16 innings is x+2 runs

Average after 16 innings = 38 + 2 =40 runs

Hence, the batsman’s average after 16 innings is 40 runs.

So, option (c) is correct.

Note: After you have applied the average formula for 15 innings, you do some changes in

the figures for 16 innings and then apply the average formula again for 16 innings. Here

remember to change the denominator from 15 in the first case to 16 in the second case as

the number of observations has increased by one.

become 15x. Now, after the 16 th innings, total runs become 15x + 70 and new average

becomes x + 2. Put these in the average formula to solve for x and then find x + 2 which is

the answer.

Complete step by step solution:

We are given that a batsman makes a score of 70 in his 16 th innings. This score increases his

average by 2 runs.

We need to find his average after the 16 th innings.

Let his average after 15 innings be x runs.

So, applying the formula for average:

\[x=\dfrac{Total Score Upto 15 Innings}{15}\]

Total score after 15 innings = 15x

Now, in his 16 th innings, he scores 70 runs and his average increases by 2 runs.

So, his new average = x+2

His total score after 16 innings = 15x + 70

We can show this by:

\[x+2=\dfrac{15x+70}{16}\]

\[16x+32=15x+70\]

\[x=38\]

So, his average after the first 15 innings was 38 runs.

Now, we are given in the question that after the 16 th innings, his average increases by 2 runs

So, his new average after 16 innings is x+2 runs

Average after 16 innings = 38 + 2 =40 runs

Hence, the batsman’s average after 16 innings is 40 runs.

So, option (c) is correct.

Note: After you have applied the average formula for 15 innings, you do some changes in

the figures for 16 innings and then apply the average formula again for 16 innings. Here

remember to change the denominator from 15 in the first case to 16 in the second case as

the number of observations has increased by one.

Last updated date: 01st Jun 2023

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