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?

12 days

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)