If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?
You will often be able to ballpark or find the exact solution by just working on the multiples of the given equations.
Say rate of work of each man is M and that of each woman is W.
Given: 12M + 16W = 1/5 (Combined rate done per day)
______3M + 4W = 1/20 (in lowest terms) ...........(I)
Given: 13M + 24W = 1/4 ......................................(II)
Reqd: 7M + 10W = ?
Using equations (I) and (II) we need to find the sum of 7M and 10W. We can get a multiple of 7M in various ways:
(3M + 4W = 1/20) * 5 gives 15M + 20W = 1/4
Adding this to equation II, we get 28M + 44W = 1/2
7M + 11W = 1/8
7 men and 11 women complete the work in 8 days. 7 men and 10 women will take a little more than 8 days to complete the work. If you do get such a question in GMAT, you will easily be able to manipulate the equations to get the desired equation. Finding the values of M and W is way too painful to interest GMAT.
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