Question

A cricket player after playing 15 matches scored 91 runs in the the 16^th match. After 16^th match, the average increased by 2.5. Find the average of runs scored after 16^th match. 
1. 51
2. 53.5
3. 51.5
4. 53

Answer 1

Correct Answer - Option 2 : 53.5

Given:

Runs scored in 16th match = 91 

Increase in average after 16th match = 2.5

Formula Used:

Average = Total runs/Number of matches

Calculations:

Let the average score after 15 matches be x.

Total runs after 15 matches = 15 × x = 15x      ----(1)

Runs scored in 16th match = 91 

Increase in average after 16th match = 2.5

⇒ Average of runs scored after 16th match = (x + 2.5)

Total runs after 16 matches = 16 × (x + 2.5) = (16x + 40)      ----(2)

From (1) and (2), we get

15x + 91 = (16x + 40) 

⇒ x = 91 - 40

⇒ x = 51

Average of runs scored after 16th match = (x + 2.5) = (51 + 2.5)

⇒ Average of runs scored after 16th match = 53.5

∴ The average of runs scored after 16th match is 53.5.