8 girls and 12 boys can complete a piece of work in 4 days, while 10 girls and 6 boys can complete it in 6 days. How long will 5 girls and 3 boys take to complete this same piece of work?
Answer & explanation
Correct answer: option 1
8G + 12B = 4 days,
32G + 48B ..(1) (Multiplied by 4 to get it done in 1 day)
10G + 6B = 6 days,
60G + 36B ..(2) (Multiplied by 6 to get it done in 1 day)
Now, (1) - (2), we get
⇒ 28G =12B
⇒ G : B = 12 : 28 = 3 : 7 (Efficiencies)
Putting efficiency in equation (1), and we get the total work
⇒ [32 (3) + 48 (7)] = 432 units.
⇒ Time required by 5 girls and 3 Boys to complete total work = \(\frac{432}{5(3)+3(7)}\) = \(\frac{432}{36}\) = 12 days, ..(\(\frac{Work}{Efficiency}\) = Time)