8 women can complete a work in 10 days and 10 children take 16 days to complete the same work. How many days will 10 women and 12 children take to complete the work?

Correct option is B

Ans. (b)
Sol.
Step 1: Work done by 8 women in 1 day = 1/10
So, work done by 1 woman in 1 day = 1/(8×10) = 1/80
⇒ Work done by 10 women in 1 day = 10 × 1/80 = 1/8
Step 2: Work done by 10 children in 1 day = 1/16
So, work done by 1 child in 1 day = 1/(10×16) = 1/160
⇒ Work done by 12 children in 1 day = 12 × 1/160 = 3/4
Step 3: Total work done by (10 women + 12 children) in 1 day
= 1/8 + 3/40
= (5 + 3)/40 = 8/40 = 1/5
Therefore, they will complete the work in 5 days.