4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work ?

4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work ?
1). 22 2/7 days
2). 25 1/2 days
3). 5 1/7 days
4). 12 7/22 days

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Guest · Answer 1 · 2019-04-06 11:14:11

Solution

Let the time taken to complete the work = $x$ days

=> $(4 M + 3 W) \times 6 = (5 M + 7 W) \times 4$

=> $24 M + 18 W = 20 M + 28 W$

=> $4 M = 10 W$ ---------------Eqn(1)

Acc to ques,

=> $(4 M + 3 W) \times 6 = (1 M + 1 W) \times x$

Using eqn(1), we get :

=> $(10 + 3) \times 6 = (\frac{10}{4} + 1) \times x$

=> $78 = \frac{7}{2} x$

=> $x = \frac{78 \times 2}{7} = \frac{156}{7}$

=> $x = 22\frac{2}{7}$ days

Guest · Answer 2 · 2019-04-18 09:18:07