Question

A batsman played n + 2 innings and got 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 38 runs in each of the first n innings. In these n innings, his average score was 30 runs and lowest score was x runs. Also, it is known that he has scored distinct number of runs in each of his innings. The smallest possible value of x is 
1. 8
2. 5
3. 6
4. 4

Answer 1

Correct Answer - Option 1 : 8

Calculation:

Total number of runs scored in (n + 2) innings = 29(n + 2) = 29n + 58

His total runs in n innings = 29n + 58 – 38 – 15 = 29n + 5

Also, his average score is 30 in these n innings,

⇒ 30n = 29n + 5

⇒ n = 5

So, the batsman has played a total of (5 + 2) = 7 innings

Total runs scored by him in 7 innings = (30 × 5) + 38 + 15 = 203

He scored less than 38 runs in each of his 5 other innnings.

So, highest possible distinct runs scored by him in the other four innings apart from the lowest score = 37, 36, 35, and 34

⇒ 38 + 15 + 37 + 36 + 35 + 34 + x = 203

⇒ x = 203 – 195 = 8

∴ The smallest possible value of x is 8