Multiple choice

12 women and 16 men can do a piece of work in 5 days. 13 women and 24 men can do it in 4 days. How long will 25 women and 50 men take to do it?

  1. 1 day

  2. 2 days

  3. 3 days

  4. 4 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let W be work per woman and M be work per man. 5(12W + 16M) = 1, so 60W + 80M = 1. 4(13W + 24M) = 1, so 52W + 96M = 1. Solving the system: 60W + 80M = 52W + 96M => 8W = 16M => W = 2M. Substituting: 60(2M) + 80M = 1 => 200M = 1 => M = 1/200, W = 1/100. For 25W + 50M: 25(1/100) + 50(1/200) = 0.25 + 0.25 = 0.5. Time = 1/0.5 = 2 days.

AI explanation

Assume the total job is 20 units. The first scenario gives 12W + 16M = 4 units per day, and the second gives 13W + 24M = 5 units per day. Multiplying the first equation by 3 gives 36W + 48M = 12, and multiplying the second by 2 gives 26W + 48M = 10. Subtracting the two yields 10W = 2, so 1W = 0.2 units. Substituting this back gives 16M = 4 - 12(0.2) = 1.6, meaning 1M = 0.1 units. The daily output of 25 women and 50 men is 25(0.2) + 50(0.1) = 10 units. Therefore, they will complete the 20-unit job in 20 / 10 = 2 days.

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