12 men and 12 women can complete a piece of work in 9 days. 6 men and 15 women can complete the same work in 12 days. How long (in days) would it take 9 women to complete half the work ?
Answer & explanation
Correct answer: option 3
12M + 12W = 9 days
108M + 108W ..(1) (Multiplied by 9 to get it in 1 day)
6M + 15W = 12 days
72M + 180W ..(2) (Multiplied by 12 to get it in 1 day)
⇒ NOW, (1) - (2), WE GET
⇒ 36M = 72W
⇒ M : W = 72 : 36 = 2 : 1 (Efficiencies)
Putting efficiency in equation (1), and get the total work
⇒ 108(2) + 108(1)
⇒ 324 units.
now the time it would take 9 women to complete half the work = \(\frac{324}{2}\) = 162 units
⇒ \(\frac{162}{9(1)}\) = 18 days.