6 men and 8 boys can finish a work in 10 days while 26 men and 48 boys

Question

6 men and 8 boys can finish a work in 10 days while 26 men and 48 boys can do the same in 2 days. How many days will 15 men and 20 boys take in completing the same work?

A) 4 days
B) 5 days
C) 6 days
D) 7 days
E) 8 days

SalahT · Accepted Answer

This is a technique used to go to the solution without solving the entire equation.
When you are given any equation and asked for the value of another equation, you can solve for each variable then calculate. 
However, in some situation given equation can be a factor or multiple of 2nd equation. In that case, it is fast and easier to use that factor to solve the question.
For example, you are given a+b = 10 a-b=2 what is 4a+4b?
Now you can solve for a and b then go for 4a+4b
or you can identify 4a+4b = 4(a+b) is a multiple of a+b and simply go to the answer by 4*10=10

now 6m+8b=10 is given and asked for 15m+20b 
you can solve m and b (since there are two different equation) then solve for 15m+20b 
or find a factor or multiple to work with.  In this case factor is a fraction. 
multiply 6m+8b=10 with 5/2 and get 15m+20b

It may seem complicated but in reality this things get very easy to identify and apply when you have practice.

SalahT · Answer

A quick and efficient solution would be,
Let,
 be the work rate of men = m
 be the work rate of boys = m
 6m+8b=10  
seems that answer can be written as a factor of a given equation  \frac{5}{2}(6m+8b) = 15m+20b 
now, multiply the work time of the equation with inverse of the multiplayer 
 10*\frac{2}{5 }=4 
Answer=A

ZulfiquarA · Answer

Make equations of the conditions given: 6/x+8/y=1/10 & 26/x+48/y=1/2
Substitute and solve: x=100 & y=200
Put the values in the third equation: 15/100+20/200=1/4 so 4 days " A "

manojfsahu · Answer

Hi Salah,

Could you please explain how you got  \frac{5}{2}

Saadman_Sakib · Answer

Hello there, Can you tell me why we inverse the fraction, please?

tareq333666 · Answer

1st condition = 10(6m+8b) here m= men & b= boys
2nd condition = 2(26m+48b)
3rd condition = X(15m+20b) here X= required time
Since the all conditions are same.
We get from 1st & 2nd conditions,
60m+80b = 52m + 96b
Or, 8m = 16b
Or, m = 2b
Now from 1st & 3rd conditions,
(60×2b)+80b = X(15×2b+20b)
Or, 200b = X (50b)
Or, X = 200b/50b
Or, X = 4 days

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Bunuel · Answer

We are equating the rates there, so it should be  6m+8b=\frac{1}{10} , not  6m+8b=10 . Hence, to get the value of  15m+20b , we multiply by 5/2 and get:

\frac{2}{5}(6m+8b)=\frac{5}{2} * \frac{1}{10} 
 15m+20b=\frac{1}{4}

Since time is the reciprocal of the rate, then 15 men and 20 boys would take 4 days to complete the same task.

SamplingCoast · Answer

given: \frac{6}{m} + \frac{8}{b} = \frac{1}{10} -----(1) 
Asked: \frac{15}{m} + \frac{20}{b} = ?

Recognise that the ratio of number of men to boys (6/8) in eq.1 is the same ratio as 15/20 = 3/4

divide eq 1 by 2 you get 
\frac{3}{m} + \frac{4}{b} = \frac{1}{20} --------(2)

multiply eq 2 by 5 to get the required value

\frac{15}{m}+ \frac{20}{b} =  5/20  
 = 1/4

no of days is the reciprocal therefore 4 days

DishaAgarwal12 · Answer

increase of 20 men and 40 boys reduce days by 8 days
increase of 10 men and 20 boys>> 4 days

therefore 15M+20B will reduce by more than 4 days
therefore 5 A is the best choice

6 men and 8 boys can finish a work in 10 days while 26 men and 48 boys

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6 men and 8 boys can finish a work in 10 days while 26 men and 48 boys

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