Multiple choice

A man does the first half of a piece of work three times faster than he does the second half. If he had done the second half also at the same rate as first, the work would have been completed 15 days earlier. In how many days has he actually completed the work?

  1. 30 days

  2. 35 days

  3. 25 days

  4. 40 days

  5. Cannot be determined

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total work be 2 units. First half (1 unit) takes time t1, second half (1 unit) takes t2. Rate1 = 3 * Rate2, so t2 = 3 * t1. Total time = t1 + 3t1 = 4t1. If second half was done at Rate1, time would be t1 + t1 = 2t1. 4t1 - 2t1 = 15 days, so 2t1 = 15, t1 = 7.5. Total time = 4 * 7.5 = 30 days.