15 men take 20 days to complete a work working 8 hours a day. How many number of hours a day should 20 men take to complete the work in 12 days?a)15 hoursb)10 hoursc)20 hoursd)12 hoursCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given Data:
- 15 men complete a work in 20 days working 8 hours a day.
- Target is to find out how many hours a day should 20 men work to complete the work in 12 days.

Calculations:
First, calculate the total work to be done:
- Let the total work be W.
- Work done by 15 men in 1 day = 1/(15*20) = 1/300 of the total work.
- Work done by 15 men in 12 days = 12/300 = 1/25 of the total work.
- Work done by 20 men in 1 day = W/20.
- Work done by 20 men in 12 days = 12W/20 = 3/5 of the total work.

Equating the work done:
- As the work done by 15 men in 12 days equals the work done by 20 men in 12 days:
1/25 = 3/5
1 = 15
- This implies that 20 men need to work 15 hours a day to complete the work in 12 days.
Therefore, the number of hours a day should 20 men take to complete the work in 12 days is 15 hours (Option A).

Answer

Formula: If M1 persons can do a piece of work in D1 days for h1 hours and M2 persons can do the same piece of work in D2 days for h2 hours,

then: M1D1h1 = M2D2h2.

In the above given problem M1=15 men, D1=20 days, h1=8 hours, M2=20 men, D2= 12 days. Substituting the above values in the formula, we get

⇒ 15 * 20 * 8 = 20 * 12 * h2;

⇒ 2400 = 240 * h2; h2 = 10 hours

Therefore, 10 hrs a day should 20 men take to complete the same work in 12 days.

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