Discussion

Question:

The average runs scored by each player, per innings, are (rounded off to the nearest integer).

Explanation:

(i) Average runs scored in the 1^st innings = 101.25
Total score = 101.25 × 4 = 405

(ii) Average runs of Virat = 108.75
Total runs of Virat = 108.75 × 4 = 435
So, the runs made by Virat in 3^rd innings = 435 - 120 - 105 - 120 = 90

(iii) Total score in the 4^th innings = 405 
Now, let Rohit’s, Pant’s and Dhawan’s scores in 4th innings be x, x and y.
⇒ 2x + y + 120 = 405
⇒ 2x + y = 285   …(1)

Let Dhawan’s and Pant’s scores in 1^st innings be p and q, respectively.
⇒ p + q + 120 + 90 = 405
⇒ p + q = 195   …(2)

From 2: 6p - x = 255   …(3) 

From 5: Dhawan’s and Pant’s scores in 2^nd innings are p - 10 and q - 10, respectively. 

⇒ Dhawan’s total runs = 330 
⇒ p + p - 15 + 90 + y = 330
⇒ 2p + y = 255   …(4)

Solving (1) and (4), we get 2x - 2p = 30   …(5)
Solving (3) and (4), we get x = 69 and p = 54

From (1) and (2),
y = 147 and q = 141

Thus, 

​​​​​​​

The average runs scored by each player, per innings = 1026/16 = 96.1875.

Hence, 96.

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