Explanation:

To solve this problem, we need to understand the concept of batting averages in cricket. The batting average is the total number of runs scored divided by the number of times a batsman gets dismissed. In this case, we are given the average after the 50th innings, which is 50.

Step 1: Calculate the total runs scored in the first 50 innings

Since the average is calculated by dividing the total runs by the number of dismissals, we can calculate the total runs scored in the first 50 innings by multiplying the average (50) by the number of dismissals.

Let's assume the number of dismissals in the first 50 innings is 'D1'.

Total runs scored in the first 50 innings = Average * Number of dismissals = 50 * D1

Step 2: Calculate the total runs scored after the 51st innings

We are given that the average after the 51st innings is 51. This means that the total runs scored after the 51st innings is equal to the average (51) multiplied by the total number of dismissals after the 51st innings.

Let's assume the number of dismissals after the 51st innings is 'D2'.

Total runs scored after the 51st innings = Average * Number of dismissals = 51 * D2

Step 3: Find the runs scored in the 51st innings

To find the runs scored in the 51st innings, we need to subtract the total runs scored in the first 50 innings from the total runs scored after the 51st innings.

Total runs scored in the 51st innings = Total runs scored after the 51st innings - Total runs scored in the first 50 innings

Total runs scored in the 51st innings = (51 * D2) - (50 * D1)

Step 4: Substitute values to find the runs scored in the 51st innings

We are given that the average in the first 50 innings is 50, so D1 is equal to 50.

We are also given that the average after the 51st innings is 51, so D2 is equal to 51.

Substituting these values into the equation:

Total runs scored in the 51st innings = (51 * 51) - (50 * 50) = 2601 - 2500 = 101

Therefore, Gavaskar made 101 runs in the 51st innings.