If 4 men and 6 boys can do a work in 8 days and 6 men and 4 boys can do the same work in 7 days, then how many days will 5 men and 4 boys take to do the same work?
Answer & explanation
Correct answer: option 2
4M + 6B = 8 days
32M + 48B ..(1) (Multiplied by 8 to get it in 1 day)
6M + 4B = 7 days
42M + 28B ..(2) (Multiplied by 7 to get it in 1 day)
⇒ NOW, (1) - (2), WE GET
⇒ 10M = 20B
⇒ M : B = 20 : 10 = 2 : 1 (Efficiencies)
Putting efficiency in equation (1), and get the total work
⇒ 32(2) + 48(1) ⇒ 112 units.
now the time it would take 5 men and 4 boys to complete the work is =
⇒ \(\frac{112}{5(2)+ 4(1)}\) = \(\frac{112}{14}\) = 8 days.