Multiple choice

If 4 men or 10 boys can do a piece of work in 12 days, working 10 hours a day, then how many days will it take to complete a piece of work thrice the previous work with 8 men and 5 boys working together for 9 hours a day?

  1. 16 days

  2. 14 days

  3. 12 days

  4. 21 days

  5. 18 days
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A Correct answer
Explanation

Using the formula (M1*D1*H1)/W1 = (M2*D2*H2)/W2, where 4 men = 10 boys, we find 1 man = 2.5 boys. The first work is 1 unit, the second is 3 units. 8 men and 5 boys equal 20 + 5 = 25 boys. Solving (10*12*10)/1 = (25*D2*9)/3 gives D2 = 16.

AI explanation

Using the equivalence of workers, 4 men equal 10 boys, so 1 man equals 2.5 boys. The team of 8 men and 5 boys is equivalent to 20 boys plus 5 boys, which is 25 boys. The total work in boy-days is 10 boys multiplied by 12 days multiplied by 10 hours, which equals 1200 boy-hours, and the new work is thrice this amount, equaling 3600 boy-hours. The number of days required is 3600 divided by the product of 25 boys and 9 hours, which equals 16 days.

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