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If 10 men or 18 boys can do a piece of work in 15 days, then 25 men

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Bunuel
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If 10 men or 18 boys can do a piece of work in 15 days, then 25 men [#permalink] If 10 men or 18 boys can do a piece of work in 15 days, then 25 men   27 Apr 2021, 05:45
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65% (02:33) correct 35% (02:23) wrong based on 243 sessions
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If 10 men or 18 boys can do a piece of work in 15 days, then 25 men and 15 boys together will do twice the work in:

(A) 4 1/2 days
(B) 9 days
(C) 8 days
(D) 32 days
(E) 36 days
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B
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LipiSinha
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Re: If 10 men or 18 boys can do a piece of work in 15 days, then 25 men [#permalink] If 10 men or 18 boys can do a piece of work in 15 days, then 25 men   27 Apr 2021, 12:01
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10 Men = 18 Boys
25 men = 45 Boys

18 Boys can do a work in 15 days
60 Boys (45 + 15) will do the work in \(\frac{(18 * 15)}{60} \)days = \(\frac{9}{2 }\)days
and twice the work in 9 days.

The answer will be B
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Re: If 10 men or 18 boys can do a piece of work in 15 days, then 25 men [#permalink] If 10 men or 18 boys can do a piece of work in 15 days, then 25 men   23 Jul 2021, 06:42
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Bunuel
If 10 men or 18 boys can do a piece of work in 15 days, then 25 men and 15 boys together will do twice the work in:

(A) 4 1/2 days
(B) 9 days
(C) 8 days
(D) 32 days
(E) 36 days
Solution:

If we let m = the rate of one man per day and b = the rate of one boy per day, we can create the equation:

10m = 1/15 and 18b = 1/15

m = 1/150 and b = 1/270

Therefore, the rate of 25 men and 15 boys per day is:

25(1/150) + 15(1/1270) = 1/6 + 1/18 = 4/18 = 2/9

So they can complete twice the work in 2/(2/9) = 9 days.

Answer: B
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Nishtha94
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Re: If 10 men or 18 boys can do a piece of work in 15 days, then 25 men [#permalink] If 10 men or 18 boys can do a piece of work in 15 days, then 25 men   08 May 2021, 01:36
Can you write this solution in detail? I am confused as to why you took 45 + 15.

LipiSinha
10 Men = 18 Boys
25 men = 45 Boys

18 Boys can do a work in 15 days
60 Boys (45 + 15) will do the work in \(\frac{(18 * 15)}{60} \)days = \(\frac{9}{2 }\)days
and twice the work in 9 days.

The answer will be B
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Re: If 10 men or 18 boys can do a piece of work in 15 days, then 25 men [#permalink] If 10 men or 18 boys can do a piece of work in 15 days, then 25 men   08 May 2021, 09:24
Nishtha94
Can you write this solution in detail? I am confused as to why you took 45 + 15.

LipiSinha
10 Men = 18 Boys
25 men = 45 Boys

18 Boys can do a work in 15 days
60 Boys (45 + 15) will do the work in \(\frac{(18 * 15)}{60} \)days = \(\frac{9}{2 }\)days
and twice the work in 9 days.

The answer will be B

That's because the question asks how many days will 25 men and 15 boys together take to complete twice the work.
Since we have already determined that 25 men is equal to 45 boys, we can rephrase the question as "how many days will 45 boys and 15 boys together take to complete twice the work?"

Hence 45 + 15.

Hope I have answered your query. :)
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Re: If 10 men or 18 boys can do a piece of work in 15 days, then 25 men [#permalink] If 10 men or 18 boys can do a piece of work in 15 days, then 25 men   08 May 2021, 19:12
Man hours = 150 = 10 men * 15 days.

Boy hours = 270 = 18 boys * 15 days.

x*(\(\frac{25}{150}\)+\(\frac{15}{270}\))=2

Question asked for 25 men, hence 25/150, and 15 boys, 15/270.

The question asked for twice the quantity of work, so equal to 2.

Ans = 9
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Re: If 10 men or 18 boys can do a piece of work in 15 days, then 25 men [#permalink] If 10 men or 18 boys can do a piece of work in 15 days, then 25 men   12 Aug 2024, 14:23
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Let's assume: Number of working units needed to complete the job=90

Then, number of units a days required to finish the job in 15 days: 90/15=6

So, 10 men or 18 boys can complete the work by making 6 unit a day during 15 days.

Each men will then be able to process: 6/10=0,1 unit a day
Each boy will then be able to process: 6/18=1/3 unit a day
The answer is B

Completing double the work would require 90*2=180 working units;
25 men and 15 boys will need t days:
(0,6*25+(1/3)*15)*t=30
t=9
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Re: If 10 men or 18 boys can do a piece of work in 15 days, then 25 men [#permalink]
12 Aug 2024, 14:23
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