3 men and 5 women together can complete a work in 6 days, whereas 4 men and 9 women together can do it in 4 days. How many women are required to do the same work in 7 days?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 12
Let 1 man's 1-day work = x
and 1 woman's 1-day work = y
3 men and 5 women together can complete a work in 6 days:
⇒ 6 × (3x + 5y) = 1
⇒18x + 30y = 1
whereas 4 men and 9 women together can do it in 4 days:
⇒ 4 × (4x + 9y) = 1
⇒ 16x + 36y = 1
On solving the above two equations: y = 1/84
Hence, 1/84 of work done by 1 woman.
Let P be the number of women required to complete the work in 7 days.
⇒ P = 84/7 = 12