Question

20 men can finish a work in 30 days.After how many days should 5 men leave the work so that th work may be finished in 35 days​

Answer 1

20 workers can finish a work in 30 days. After how many days should 5 workers leave the job so the work is completed in 35 days?

First of all we convert it in unit like this

20 workers × 30 days = 600 units work

After leave the 5 workers , we have 35 days for complete the work.

In 35 days only 15 workers will do the work.

So the work completed in 35 days by 15 workers = 35 ×15 =525 units

Remaining unit = 600 -525 =75 units

This units would done by 5 workers in ( 75/5) = 15 days .

So after 15 days 5 workers should leave the job.

Total unit of work = 20 men x 30 days = 600 Man-Days

So, 20 men working for 1 day will do 1/30 part of the job.

So, 1 man working for 1 single day will do 1/(30*20) = 1/600 part of the job.

Now, let us assume that 5 people leave after x days.

So, as per the question, 20 men worked for x days and 15 men worked for (35-x) days.

So, to form an equation,

20x/600 + 15(35-x)/600 = 1

=> 20x + 525 - 15x = 600

=> 5x = 75

=> x = 15

So, the 5 men left after 15 days.