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A man whose bowling average is 12.4 takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets, taken by him before his last match is:Options :85787264

Question

A man whose bowling average is 12.4 takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets, taken by him before his last match is:Options :85787264

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Solution

Let's solve this step by step:

  1. The man's average after taking 5 wickets for 26 runs is 12.4 - 0.4 = 12.0
  2. This means that for all the wickets he has taken so far, he has given away an average of 12.0 runs per wicket.
  3. In his last match, he took 5 wickets for 26 runs, which means he gave away an average of 26/5 = 5.2 runs per wicket.
  4. The difference between his overall average and the average for the last match is 12.0 - 5.2 = 6.8
  5. This difference is due to the 5 wickets he took in the last match. So, the total number of runs that increased his average is 6.8 * 5 = 34.
  6. Before the last match, his average was 12.4. So, the total number of runs he had given away until then is 12.4 * number of wickets.
  7. After the last match, the total number of runs he has given away is (12.4 * number of wickets) + 34.
  8. But we know that this total number of runs is also equal to 12.0 * (number of wickets + 5).
  9. So, we can set up the equation: 12.4 * number of wickets + 34 = 12.0 * (number of wickets + 5)
  10. Solving this equation gives us the number of wickets he had taken before the last match.

Let's solve the equation:

12.4w + 34 = 12.0w + 60 0.4w = 26 w = 26 / 0.4 w = 65

So, the man had taken 65 wickets before his last match. The correct option is not listed in the given options.

This problem has been solved

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