@Sumiran, Typo.. equating (3) and (4), it should be solving (3) and (4)… right ?

Another short method for time saving in exam :-

”3 men and 4 women can complete a work in 10 days by working 12 hours a day. 13 men and 24 women can do the same work by working same hours a day in 2 days.”

Means, $(3M+4W)*10*12=(13M+24W)*2*12$ (Where, M= men and W= women)

$\Rightarrow M=2W$

Now, “How much time would 12 men and 1 women working same hours a day will take to complete the whole work?”

Suppose, it takes ‘d’ days to complete the same work by 12 men and 1 women.

So, $(12M+1W)*d*12 = (3M + 4W)*10*12$

Put, $M=2W$,

$25W*d = 10W *10 $ $\Rightarrow d= 4$

Another short method for time saving in exam :-

”3 men and 4 women can complete a work in 10 days by working 12 hours a day. 13 men and 24 women can do the same work by working same hours a day in 2 days.”

Means, $(3M+4W)*10*12=(13M+24W)*2*12$ (Where, M= men and W= women)

$\Rightarrow M=2W$

Now, “How much time would 12 men and 1 women working same hours a day will take to complete the whole work?”

Suppose, it takes ‘d’ days to complete the same work by 12 men and 1 women.

So, $(12M+1W)*d*12 = (3M + 4W)*10*12$

Put, $M=2W$,

$25W*d = 10W *10 $ $\Rightarrow d= 4$