Question

7 men and 16 women complete a work in 15 days then how many days can 5 men and 8 women complte the same work

Answer 1

Find 1 man’s one day contribution to work.

How?

As follows…

7 men each working for 15 days so total man days is 7 * 15 = 105

So 1 man’s 1 day contribution is 1/105.

Similarly, 16 women each working for 15 days.

Hence, 16 * 15 = 240

Therefore, 1 woman’s 1 day contribution is 1/240.

Now the easy part.

1 man’s per day contribution is 1/105 hence, 5 mens’ contribution per day would be 5 * 1/105 = 5/105 = 1/21

Similarly, 1 woman’s per day contribution is 1/240, hence 8 womens per day would be 8 * 1/240 = 8/240 = 1/30

Now, adding contribution of 5 men and 8 women per day, we get

1/21 + 1/30 = 17/210.

Hence, total time taken would be reciprocal of the total per day contribution i.e. 210/17 which is equal to 12 7/20 days.

Hope this helps.