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# If 4 boys or 3 men can complete a piece of work in 10 days how many da

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Re: If 4 boys or 3 men can complete a piece of work in 10 days how many da [#permalink]
4 boys = 3 men
1 boys = ¾ men
3 boys = (¾) * 3 men
= 9/4 men
4 men + 3 boys = 4 men + 3 boys = 4 men + 9/4 men = 25/4 men

3 men can complete a work in 10 days

25/4 men can complete a work in (10 x 3)*4/25 = 24/5 days (A)
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Re: If 4 boys or 3 men can complete a piece of work in 10 days how many da [#permalink]
3Men= 4 boys
M/B=4/3
4m+3B=4x4/3B+3B
=25/3B
now
(25/3)Bx T=4Bx10 (T= no of days)
T=24/5
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Re: If 4 boys or 3 men can complete a piece of work in 10 days how many da [#permalink]
CrackverbalGMAT wrote:
Completion of work, or work that is completed is = 1

Work done by 4 Boys in 10 days = 1

Work done by 4 Boys in 1 day = $$\frac{1}{10}$$

Work done by 1 Boys in 1 day = $$\frac{1}{10 * 4}$$ = $$\frac{1}{40}$$

Similarly, Work done by 3 Men in 10 days = 1

Work done by 3 Men in 1 day = $$\frac{1}{10}$$

Work done by 1 Man in 1 day = $$\frac{1}{10 * 3}$$ = $$\frac{1}{30}$$

Therefore work done in 1 day by 3 Boys and 4 Men = $$3 * \frac{1}{40} + 4 * \frac{1}{30}$$ = $$\frac{9 + 16}{120} = \frac{25}{120} = \frac{5}{24}$$

The number of days = Inverse of the work done in 1 day = $$\frac{24}{5}$$

Option A

Arun Kumar

I am not convinced with your calculations. Can you please elaborate on that? and please explain why we can not assume that all boys and men work at the same exact constant speed. Then the answer would be the same 10 days.

Bunuel could you also elaborate on this?

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Re: If 4 boys or 3 men can complete a piece of work in 10 days how many da [#permalink]
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Work= Rate * time

Lets assume work=1
4 Boys can finish 1 in 10 days. Rate of 4 boys= 1/10
Rate of 1 Boy= 1/40
Similarly rate of 1 Men=1/30.

Let's assume time t to finish work 1 by 3 boys and 4 men.
Work=R*t
1= t(3/40+4/30) ->t(25/120)=1 -> t=120/25 -> t->24/5