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If 4 men and 6 boys can do a work in 8 days and 6 men and 4 boys can do the same work in 7 days, then how many days will 5 men and 4 boys take to do the same work?

If 4 men and 6 boys can do a work in 8 days and 6 men and 4 boys can do the same work in 7 days, then how many days will 5 men and 4 boys take to do the same work? Correct Answer 8

Given:

4 men and 6 boys can do a work in 8 days

6 men and 4 boys can do the same work in 7 days

Concept used:

Time = Work/Efficiency

Calculation:

Let, M = Men; B = Boys

(4M + 6B) × 8 = (6M + 4B) × 7

⇒ 32M + 48B = 42M + 28B

⇒ 42M - 32M = 48B - 28B

⇒ 10M = 20B

⇒ M/B = 2/1

So, the efficiency of one man = 2

Efficiency of one boy = 1

Total work = × 8 = 14 × 8 = 112

Efficiency of 5 men and 4 boys = (5 × 2) + (4 × 1) = 10 + 4 = 14

Required time to finish the work = 112/14 = 8 days

∴ The 5 men and 4 boys will take 8 days to do the same work

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