# Time and Work Questions Shortcut trick #4 Men and Boys

This time we are solving questions on Time and Work in which Men, Women or Boys are given and we have to determine in how much time they will do the work together.

Suppose we are given a question on Men and Boys work like the one given below in which we are given:-

2 men and 3 boys does a work in 10 days while 3 men and 2 boys can also perform the same task in 8 days. So determine in how many days can 2 men and 1 boy can do that work?
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Solution:-

Let 1 man does the work in m days and one boy does the work in b days

So according to the given condition in one day 1/m or M part of the work is done by 1 man and in one day 1/b or B part of the work is done by 1 boy.

According to the question we have 2 * (1/m) + 3 * (1/b) = 1/10.....................(A)

Or we have 2 M + 3 B = 1/10.....................(A)

or (2M+3B)*10=1

(work done by 2 men and 3 boys in one day)

We also have 3 M + 2 B = 1/8.....................(B)

(3M+2B)*8=1

Equating the above two equations, we get

M=(7/2)B............(C)

putting the value of M in equation (A), we get

B=1/b = 1/100 and

putting the value of B in equation (c), we get

M=1/m = 7/200

We have to find how many days will 2 men and 1 boy take to complete the work.

so putting the values of M and B in equation (A), we get

work completed in one day by 2 men and 1 boy = (2 * 7/200) + 1/100 => 8/100 => 1/12.5

So the work will be completed in 12.5 days.

the shortcut trick in this type of question is that you should start from the equating the two equations step directly. Means as you read this type of question in the exam. right then

write the equations like in this question.

(2M+3B)*10=(3M+2B)*8

you can write down these equations as soon as you read the question and solve them faster.