Question 48

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 ?

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

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