Time and work Quantitative aptitude question

[Q] 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.
(a) 5 days
(b) 2 days
(c) 4 days
(d) 6 days

Solution

Answer   (c)
Explanation
----
Let work done by 1 man in 1 day = m,
work done by 1 woman in 1 day = w

Work done by 6 men and 8 women in 1 day = 1/10

=> 6m + 8w = 1/10

=> 60m + 80w = 1 ------ (1)

Work done by 26 men and 48 women in 1 day = 1/2

=> 26m + 48w = ½

=> 52m + 96w = 1 ------  (2)

Solving equation 1 and equation 2. We get m = 1/100 and w = 1/200

Work done by 15 men and 20 women in 1 day

= 15/100 + 20/200 =1/4

=> Time taken by 15 men and 20 women in doing the work = 4 days