Question

In Group A, 5 men or 10 women or 15
children can do a work in 87 days
while in group B, 10 men or 15 women
or 20 children can do a work in 98
days. If Group A workers started the
work taking 10 men and 15 women
and 20 children together and after
4 days, group B workers joined them
with their 15 men and 20 women
and 25 children, in how many
days the work will complete?​

Answer 1

Answer:

Answer 5 days

Explanation :

The total work can be finished by in 7 days if 5 men work each day.

Therefore, one man can finish the work by 7x5 = 35 days.

If this work is shared by 7 workers the work can be finished in 35/7 = 5 days.

Another method:

To complete the work, we note that when the number of workers increases, the number of days decreases.

Therefore the ratio between number of workers and number of days is in inverse proportion.

If the number of days required corresponding to 7 men is y, then we get (by reversing the second ratio)

5 : 7 :: y : 7

Hence 7y=5x7

(since the product of means equals to that of extremes)

Therefore y = 5.

Another method :

7 men finish the work in 5 days.

Therefore, in one day 7 men can complete 1/5 th portion of the work.

Hence 1 man in 1 day can complete 1/(5x7) th portion of the total work.

Therefore, in one day 7 men can finish 7x(1/(5x7)) = 1/5 th portion of the total work.

Hence they will take 5 days to finish the job.