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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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Bunuel
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If 4 boys or 3 men can complete a piece of work in 10 days how many da [#permalink] New post   10 Jan 2020, 02:34
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If 4 boys or 3 men can complete a piece of work in 10 days how many days will it take for 4 men and 3 boys to finish the work?

A. 24/5
B. 4
C. 24/7
D. 3
E. 8/3
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A
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If 4 boys or 3 men can complete a piece of work in 10 days how many da [#permalink] New post   10 Jan 2020, 20:16
Bunuel wrote:
If 4 boys or 3 men can complete a piece of work in 10 days how many days will it take for 4 men and 3 boys to finish the work?

A. 24/5
B. 4
C. 24/7
D. 3
E. 8/3


Method 1:
Given, 4/b = 10 & 3/m = 10
—> 1/b = 1/40 & 1/m = 1/30

Work done by 4 men and 3 boys in a day
= 4/m + 3/b = 4/30 + 3/40
= (4*4 + 3*3)/120 = 25/120 = 5/24

Time required to complete the work = 24/5

IMO Option A


Method 2:
4 boys can complete the work in 10 days
—> 1 boy can complete the work in 40 days

Similarly, 1 man can complete the work in 30 days.

Let the total work = LCM(40, 30) = 120 units
—> Rate of 1 boy = 120/40 = 3 units/day
& Rate of 1 man = 120/30 = 4 units/day

Rate of 4 men & 3 boys = 4*4 + 3*3 = 25 units/day
—> Time talen to complete the same work = 120/25 = 24/5 days

IMO Option 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] New post   10 Jan 2020, 23:50
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] New post   25 Aug 2020, 07:26
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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

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Re: If 4 boys or 3 men can complete a piece of work in 10 days how many da [#permalink] New post   25 Aug 2020, 07:43
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] New post   05 Mar 2022, 13:53
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] New post   06 Mar 2023, 14:54
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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
Answer 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]
06 Mar 2023, 14:54
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