Question

The average of runs of a cricket player of 10 innings was 32. How many runs must he take in his next innings so as to increase his average of runs by 4?
(A) 2
(B) 4
(C) 70
(D) 76

Answer 1

Hint:- We use the concept of average, to find out the total number of runs scored by the player in 10 and 11 innings respectively. Once that is done, we can find out the runs scored in the 11th inning.

Complete step-by-step answer:
From the question, we know that the average runs of a cricket player in 10 innings was 32.
From this given information, we can calculate the total number of runs the cricket player scored in 10 innings.
Total number of runs scored in 10 innings = average runs scored $ \times $ number of innings
Thus, we get,
Total runs in 10 innings by the cricket player to be equal to 32 × 10 = 320 runs
Now as per the question we know that the cricket player’s average increased by 4 runs after the player scored “x” number of runs in the 11th innings.
Hence the new average runs scored by the cricket player in 11 innings = 32 + 4 = 36 runs
Thus, the total runs scored by the cricket player in 11 innings = 36 × 11 = 396 runs
Runs made in the 11th inning = Total runs scored in 11 innings – total runs scored in 10 innings
Hence runs made in the 11th inning = 396−320 = 76 runs

The correct option is (D)

Note:- To find the average of a group of numbers, divide the sum of numbers by the total number of events.
Average = Sum of events by total number of events. Average can be calculated only for similar quantities and not for dissimilar quantities. Average of height and weight cannot be calculated. It should either be the average height of all students or average weight of all students.