Question

3m and 4w can complete a work in 16 days while 4m and 3w can complete the same work in 12 days. Then find 7m and 7w can complete same work in how many days?​

Answer 1

. 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. :)

Answer 2

Answer:

3m + 4w - 16 days

4m + 3w - 12 days

so, (3m + 4w) 16= (4m + 3w) 12

48m + 64w = 48m + 36w

28w= 0

therefore w = 0

so (3m + 0) 16= (4m + 0) 12

3 men can complete the work in 16 days

total work = 3×16= 48 unit

Hence 7m +7w = 7m + 0

so, 7m + 7w can complete the work in 48/7 days.