Question

2 men and 5 boys can finish a piece of work in 4 days, while 3 men and
6 boys can finish it in 3 days. Find the time taken by one man alone to
finish the work and that taken by one boy alone to finish the work.​

Answer 1

Let the work done by a man be x.
Let the work done by a boy be y.

Work done in one day by man= 1/x
Work Done in one day by boy= 1/y

A.T.Q.
2/x + 5/y =1/4 - Eqn 1
3/x + 6/y =1/3 - Eqn 2

Now, Let 1/x be a and 1/y be b.

2a +5b=1/4 - Eqn 3
3a +6b=1/3 - Eqn 4

Solve the following equations by Elimination method and get the values as a= 1/18 and b= 1/36

Now x = 18 days and y = 36 days (Put values of a = 1/x and b=1/y)

Thus 1 man alone can do the work in 18 days while 1 day takes 36 days to do the same work.
Hope it helps you...