Question

57. 2 MEN AND 3 BOYS CAN DO A PIECE OF WORK IN 10 DAYS WHILE 3 MEN AND 2 BOYS CAN DO THE SAME WORK IN 8 DAYS. IN HOW MANY DAYS CAN 2 MEN AND 1 BOY DO THE WORK?

Answer 1

Let 1 men's 1-day work = x.

Let 1-boy's 1-day work = y.

Given that 2 men and 3 boys can do a piece of work in 10 days.

2x + 3y = 1/10   ----- (1)

Given that 3 men and 2 boys can do a piece of work in 8 days.

3x + 2y = 1/8  ------ (2)


On solving (1) * 3 & (2) * 2, we get

6x + 9y = 3/10

6x + 4y = 1/4
-------------------

         5y = 2/40

         5y = 1/20

          y = 1/100   ----------- (3)


Substitute (3) in (1), we get

2x + 3y = 1/10

2x + 3(1/100) = 1/10

2x + 3/100 = 1/10

2x = 7/100

x = 7/200.


Therefore 2Men + 1Boy = 2(7/200) + 1(1/100)

                                        = 7/100 + 1/100

                                        = 8/100

                                        = 2/25

                                        = 12 1/2 days.


Therefore 2 men and 1 boy can do the work in 12 1/2 days.


Hope this helps!