Q) 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

a) 35 days              b) 40 days               c) 45 days                     d) 50 days

Ans:

Let m be the work done by a man in 1 day and b be the work done by a woman in 1 day

Hence, by given 1st condition: 4 m + 6 w = 1/8 ………… (i)

and by given 2nd condition: 3 m + 7 w = 1/10 ……………..(ii)

Since in question, we need to find the work done by women, let’s solve the above equations for value of w and dissolve m

To solve, let’s multiply 1st equation (i) by 3, (ii) by 4 and subtract former from latter:

4 x (3 m + 7 w = 1/10) – 3 x (4 m + 6 w = 1/8)

∴ 12 m + 28 w – 12 m – 18 w = 4/10 – 3/

∴ 10 w = 1/40

∴ w = 1/400

∴ Now, work done by 10 women in 1 day = 1/400

∴ work done by 10 women in 1 day: 10 w = 10 x 1/400 = 1/40

Since time taken by 10 women  together to finish 1/40 work = 1 day

∴ time taken by 10 women together can finish full work = 1/(1/40) = 40 days