​35 men and 49 women, working together, can do a job in 84 days while 48 men and 84 women, working together, can do the same job in 56 days. In how many days can the same job be done by 30 men and 21 women, working together? ​

Correct option is B

Given:

35 men and 49 women can complete the job in 84 days.

48 men and 84 women can complete the same job in 56 days.

Formula Used:

Total work = Total Time $$\times$$ Efficiency

Solution:

Let, Man → M; Woman → W

35 M + 49 W = 84 days

48 M + 84 W = 56 days 

Therefore,

84 (35 M + 49 W) = 56 (48 M + 84 W)

=> 3 (35 M + 49 W) = 2 (48 M + 84 W)

​=> 105 M + 147 W = 96 M + 168 W

=> 9 M = 21 W

=> $$\frac {M}{W} = \frac{7}{3}$$​​

Total Work = (35 $$\times$$ 7 + 49 $$\times$$ 3) $$\times$$ 84 

= 392 $$\times$$​84 = 32928

Work done by 30 men and 21 women:

Total Efficiency = 30$$\times$$​7 + 21 $$\times$$​ 3 

= 210 + 63 = 273

Total Time = $$\frac{32928}{273}$$ = $$120\frac{8}{13}$$ dyas

Thus, the correct option is (b)