Question

8 girls and 12 boys can finish work in 5 days while 6 girls and 8 boys can finish it in 7 days. Find the time taken by the one girl alone that by one boy alone to finish the work​

Answer 1

Answer:

A girl alone takes 70 days to finish the work.

A boy alone takes 140 days to finish the work.

Step-by-step explanation:

Let a be the fraction of the work done by a girl in one day.

Let b be the fraction of the work done by a boy in one day.

Then the fraction of the work done by 8 girls in one day is 8a, and the fraction done by 12 boys in one day is 12b.  Together, the fraction done in one day is 8a+12b.  Since they take 5 days to finish the work, this gives

• 8a + 12b = 1/5      ...(1)

Similarly, the second piece of information gives

• 6a + 8b = 1/7      ...(2)

Dividing (2) by 2 gives 3a+4b=1/14, and multiplying this by 3 gives

• 9a + 12b = 3/14      ...(3)

Subtracting (1) from (3) gives

• a  =  3/14 - 1/5  =  15/70 - 14/70  =  1/70.

To get b, put this into any of the equations above.  Let's use 3a+4b=1/14:

• 3/70 + 4b = 1/14  ⇒  4b = 5/70 - 3/70  = 2/70  ⇒  b = 1/140.

The fraction done by a girl in one day is 1/70, so a girl alone takes 70 days to finish the work.

The fraction done by a boy in one day is 1/140, so a boy alone takes 140 days to finish the work.

Hope this helps.