XAT 2024 — QA & DI Question 23
Read the following scenario and answer the THREE questions that follow.
A T20 cricket match consists of two teams playing twenty overs each, numbered 1 to 20. The runs scored in any over is a non-negative integer. The run rate at the end of any over is the average runs scored up to and including that over, i.e., the run rate at the end of the k-th over is the average number of runs scored in overs numbered 1, 2, …, k, where 1 ≤ k ≤ 20, k a positive integer. The following table indicates the run rate of a team at the end of some of the overs during a T20 cricket match (correct up to 2 decimal places), where 1 ≤ N – 2 < N + 6 ≤ 20, N a positive integer. It is also known that the team did not score less than 6 runs and more than 15 runs in any over.
| Over Number | Run Rate |
| N - 2 | 8.00 |
| N | 7.43 |
| N + 2 | 8.11 |
| N + 4 | 8.45 |
| N + 6 | 8.08 |
What is the value of N?
Answer & solution
7
- B
13
- C
14
- D
9
- E
12
Average runs scored till Nth over is 7.43.
∴ Total runs scored in N overs = N × 7.43.
It would be best to check the options for the value of N such that N × 7.43 should be an integer.
This is possible for option (a) i.e., 7 and option (c) i.e., 14.
Now, the runrate at the end of N + 6 overs is 8.08. Checking for N = 7 or 14 such that (N + 6) × 8.08 should be an integer.
N = 7 is the only option satisfying.
⇒ N = 7
Runs scored after:
5th over: 5 × 8 = 40
7th over: 7 × 7.43 = 52
9th over: 9 × 8.11 = 73
11th over: 11 × 8.45 = 93
13th over: 13 × 8.08 = 105
Hence, option (a).