Question

13. 12 men and 8 women can do a piece of work in 16 days. 13 men and 4 women can do it in 18 days.
How long will 3 men and 12 women take to do it?






14. 10 men and 15 women can do a piece of work in 6 days. 12 men and 27 women can do the same
work in 4 days. How long will 6 men and 11 women take to do it?​

Answer 1

Step-by-step explanation:

Others have already given the answer. I will use Unitary Method to solve this question.

We are given that 3 men do the work in 16 days.

So, Work done by 3 men in 1 day =1/16

Now, Work done by 1 man in 1 day = 1/(16∗3)=1/48 days.

Similarly, Work done by 1 woman in 1 day can be found out and it is 1/64

Now, Work done by 12 men in 1 day = 12/48=1/4

Work done by 8 women in 1 day = 8/64=1/8 .

Now, Work done 12 men and 8 women in 1 day = 1/4+1/8=3/8

So, 12 men and 8 men do 3/8 of work in 1 day.

So, to complete the work, it will take them 8/3 days. We Just inverse the fraction found above. This is the beauty of Unitary Method.

So, the total time taken is 8/3 days = 2 Days 16 Hrs

Hope that helps. :)

Here is how it is solved:

5(12 M + 16 W) = 4(13 M + 24 W)

60M + 80W = 52M + 96W

That gives, 8M = 16W, which is , 1M=2W

Now, 12 M + 16W can do work in 5 days.

So, 12 M + 8 M can do work in 5 days.

So, 20M can do work in 5 days.

Now, 7M + 10W = 7M + 5M = 12 M

Hence, if 20M can do work in 5 days, 12M can do work in (20*5)/12 = 8.33 days.