Question

6 men and 8 women can do a work in 40 days. 8 men and 16 women finish the same work in 24 days. In how many days can 10 men and 8 women finish the same work?
(1) 16
(2) 24
(3) 28
(4) 30

Answer 1

answer : option (d) 30

explanation : (6 men + 8 women ) can do a work in 40 days

(8 men + 16 women) can do the same work in 24 days.

so, use formula, $N_1W_1=N_2W_2$
where N denotes number of people ( men and women) and W denotes number of days

so, 40(6men + 8women) = 24(8men + 16women)

or, 240men + 320 women = 192men + 384women

or, 48men = 64 women

or, 3men = 4women

hence, 1 man = 4/3 women

so, (6 men + 8 women ) can do work in 40 days

or, (6 × 4/3 women + 8 women ) can do work in 40 days

or, 16 women can do work in 40 days

or, 1 woman can do work in 40 × 16 = 640 days

now, we have to find number of days in which 10 men and 8 women do work

so, (10men + 8 women) = (10 × 4/3 + 8) women
= (64)/3 women

as 1 woman can do work in 640 days

so, 64/3 women can do the same work in 640/(64/3) = 30 days

hence, option (d) is correct