The batting average of a particular batsman is 60 runs in 46 innings.If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs,find his highest score.179208210None of these

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

Step 1: Calculate the total runs scored by the batsman in all 46 innings. This is done by multiplying the average by the number of innings. So, 60 runs/inning * 46 innings = 2760 runs.

Step 2: Calculate the total runs scored by the batsman in the 44 innings excluding his highest and lowest scores. This is done by multiplying the new average by the number of these innings. So, 58 runs/inning * 44 innings = 2552 runs.

Step 3: Subtract the total runs scored in the 44 innings from the total runs scored in all 46 innings to find the sum of the highest and lowest scores. So, 2760 runs - 2552 runs = 208 runs.

Step 4: We know that the difference between the highest and lowest scores is 150 runs. So, if we add this difference to the lowest score, we should get the highest score. Let's denote the lowest score as L and the highest score as H. We have two equations here:

H + L = 208 (from step 3) H - L = 150 (given in the problem)

We can solve these two equations simultaneously to find the values of H and L. Adding the two equations gives:

2H = 358

So, H = 358 / 2 = 179 runs.

Therefore, the highest score of the batsman is 179 runs.