Instructions

Directions for the following two questions: Answer the questions based on the following information.

The batting average (BA) of a Test batsman is computed from runs scored and innings played — completed innings and incomplete innings (not out) in the following manner:

$$r_1 =$$ Number of runs scored in completed innings

$$n_1 =$$ Number of completed innings

$$r_2 =$$ Number of runs scored in incomplete innings

$$n_2 =$$ Number of incomplete innings

$$BA=\frac{r_1+r_2}{n_1}$$

To better assess a batsman’s accomplishments, the ICC is considering two other measures $$MBA_1$$ and $$MBA_2$$ defined as follows:

$$MBA_1 = \frac{r_1}{n_1} + \frac{n_2}{n_1}*max[0,(\frac{r_2}{n_2}-\frac{r_1}{n_1})]$$

$$MBA_2 = \frac{r_1 + r_2}{n_1 + n_2}$$

Question 1

Based on the above information which of the following is true?

Solution

Lets take $$n_1 = n_2 = 10$$ and $$r_1 = r_2 =100$$ .
Using given formula we have $$BA = 20$$ and $$MBA_1 = MBA_2 = 10$$ .
So we have $$BA$$ highest which is not the case in option A,B and C. Hence the correct option is D.

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