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If 16 men and 12 boys can do a piece of work in 5 days, 24 men and 13 boys can do it in 4 days. In how many days will 16 men and 17 boys complete the work?


1. 5 days 
2. 3 days 
3. 4 days 
4. 2 days 

1 Answer

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Best answer
Correct Answer - Option 3 : 4 days 

Formula used:

M1 × D1 = M2 × D2

Here M is any person, who is doing the work and D is the time taken to do the work

Concept used:

Here M1 and M2 is the efficiency of the person who is doing the work

Calculation:

Let the required time taken be y days

For notation, Men = M and Boy = B

M1 × D1 = M2 × D2

⇒ (16M + 12B) × 5 = (24M + 13B) × 4 = (16M + 17B) × y

Taking the first two equations

⇒ (16M + 12B) × 5 = (24M + 13B) × 4

⇒ 80M + 60B = 96M + 52B

⇒ 8B = 16M

⇒ B = 2M

Taking the last two equations

⇒ (24M + 13B) × 4 = (16M + 17B) × y

⇒ 96M + 52B = (16M + 17B) × y

⇒ 96M + 104M = (16M + 34M) × y

⇒ 200M = 50M × y

⇒ y = 4

∴ Required time taken to do the work is 4 days

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