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In a certain number of innings, the average runs scored by a batsman were 34. He scored 119 runs in the next innings and his average to 39. What is the total number of innings played by the batsman?Options1913111715

Question

In a certain number of innings, the average runs scored by a batsman were 34. He scored 119 runs in the next innings and his average to 39. What is the total number of innings played by the batsman?Options1913111715

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Solution

To solve this problem, we can use the formula for calculating the average, which is the total sum of values divided by the number of values.

Step 1: Let's denote the initial number of innings as 'x'. The total runs scored in these innings would be 34x (since the average was 34).

Step 2: After the batsman scored 119 runs in the next innings, the total runs became 34x + 119.

Step 3: The new average after this innings is 39. So, we can set up the equation: (34x + 119) / (x + 1) = 39.

Step 4: Solving this equation will give us the value of 'x', which is the initial number of innings.

Let's solve it:

34x + 119 = 39x + 39 119 - 39 = 39x - 34x 80 = 5x x = 80 / 5 x = 16

So, the batsman had initially played 16 innings.

Step 5: Adding the next innings in which he scored 119 runs, the total number of innings played by the batsman is 16 + 1 = 17.

So, the correct option is 17.

This problem has been solved

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