Multiple choice

P does 40% of a piece of work in 10 days. He then calls Q and they together finish the remaining work in 9 days. How long will Q alone take to complete the whole work?

  1. 35.5 days

  2. 25 days

  3. 29 days

  4. 37.5 days

  5. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P does 40% in 10 days, so P's rate is 4% per day. Remaining work is 60%. P and Q finish 60% in 9 days, so their combined rate is 60/9 = 6.66% per day. Q's rate = 6.66 - 4 = 2.66% per day. Time for Q = 100 / 2.66 = 37.5 days.

AI explanation

Using the unitary method, P completes 40% of the work in 10 days, meaning P's daily rate is 0.4 divided by 10, or 1/25 of the work per day. The remaining work is 60%, which P and Q complete in 9 days, giving them a combined daily rate of 0.6 divided by 9, or 1/15 of the work per day. Q's daily rate is found by subtracting P's rate from their combined rate: 1/15 minus 1/25, which equals 2/75 of the work per day. Therefore, Q alone will complete the whole work in 75 divided by 2 days, resulting in 37.5 days.

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