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

Question

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

ScottTargetTestPrep · Accepted Answer

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

LipiSinha · Answer

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

Nishtha94 · Answer

Can you write this solution in detail? I am confused as to why you took 45 + 15.

LipiSinha · Answer

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.

twobagels · Answer

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

Nicolass · Answer

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

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