Multiple choice

A contractor Abhay Singh employed some men to do a piece of work which can be done by 16 men in 14 days.At the end of 5 days, 7 of the men stopped working and 3 days later half of the remainder stopped working; the rest finished the work in 5 days.What is the number of men originally employed?

  1. $25$
  2. $27$
  3. $29$
  4. $33$
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A Correct answer
Explanation

Let x be the number of men. Total work = 16 * 14 = 224 man-days. Work done in first 5 days = 5x. Remaining work = 224 - 5x. After 7 men leave, x-7 men work for 3 days. Then (x-7)/2 men work for 5 days. Setting up the equation: 5x + 3(x-7) + 5((x-7)/2) = 224. Solving this yields x = 25.

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