Question

A batsman was having 32 runs per innings as his average after the 15th innings. His average increased by 2 runs after the 16th inning. Then what was his score in the 16th inning?

• A. 64
• B. 60
• C. 46
• D. 62

Hint:

Use total runs before and after: new total minus old total gives the 16th innings score.

Answer 1

The Correct Option is A

To solve the problem, we will use the concept of averages and simple arithmetic calculations. Let's go through the solution step-by-step:

1. Initially, the batsman had played 15 innings with an average of 32 runs per inning. Thus, the total runs scored in these 15 innings can be calculated as follows: \(Total\ Runs\ for\ 15\ innings = 15 \times 32 = 480\)
2. After the 16th inning, the batsman's average increased by 2 runs, making the new average 34 runs per inning. This new average is calculated based on 16 innings. \(New\ Total\ Runs\ for\ 16\ innings = 16 \times 34 = 544\)
3. To find out the score in the 16th inning, we subtract the total runs after 15 innings from the total runs after 16 innings: \(Score\ in\ 16th\ inning = 544 - 480 = 64\)

The batsman's score in the 16th inning was 64. 

This confirms that the correct option is 64.

Answer 2

Step 1: Find the total runs from the first 15 innings.
The batsman's average after 15 innings is 32 runs. So his total runs from these innings is \(32 \times 15 = 480\).

Step 2: Find the new total after 16 innings.
His average goes up by 2 runs after the 16th innings, so the new average is \(32 + 2 = 34\). The total runs after 16 innings is \(34 \times 16 = 544\).

Step 3: Find the score in the 16th innings.
The score in the 16th innings is the difference between the two totals: \(544 - 480 = 64\).

Final Answer:
The batsman scored 64 runs in the 16th innings. \[ \boxed{64} \]