GMAT Math

If 3 men or 4 women can build a wall in 43 days , then in how many days can 7 men and 5 women build this wall. Explain with formulae etc - Does Ratio MDH/W apply where M is Men , D is Days H is hours , W is Work

Let's call rate of 1 Man = Rm and
rate of 1 Woman = Rw

We know, Rate * Time = Work

Here, 3Rm (43) = 1 and 4Rw (43) = 1 So,
Rm = 1 / (3 * 43) and Rw = 1 / (4 * 43)

Combined rate of 7 Men = 7 / (3 * 43)
Combined rate of 5 Women = 5 / (3 * 43)

So combined rate of 7 men and 5 women, Rc = 7 / (3 * 43) + 5 / (3 * 43)
which is 1 / 12

so, since RT = W; (1 / 12) * T = 1 so time taken by 7men and 5women = 12 Days.

Hope this helps...

sumgb wrote:Let's call rate of 1 Man = Rm and
rate of 1 Woman = Rw

We know, Rate * Time = Work

Here, 3Rm (43) = 1 and 4Rw (43) = 1 So,
Rm = 1 / (3 * 43) and Rw = 1 / (4 * 43)

Combined rate of 7 Men = 7 / (3 * 43)
Combined rate of 5 Women = 5 / (4 * 43)

So combined rate of 7 men and 5 women, Rc = 7 / (3 * 43) + 5 / 4 * 43)
which is 1 / 12

so, since RT = W; (1 / 12) * T = 1 so time taken by 7men and 5women = 12 Days.

Hope this helps...

Very good explanation. there is a little typo

Thanks Ozlemg, lazy cut and paste on my behalf!!

Could you please explain how did you come up with

7 / (3 * 43) + 5 / 4 * 43)

= 1/12 ?

Thanks for your help.

Get your lowest common denominator = 3*4*43

then (7*4)/(3*4*43) = (5*3)/(3*4*43) = 28/(3*4*43) + 15/(3*4*43) = 43/(*3*4*43) = 1/12