# 20 men can do a piece of work in 24 days. After working for 6 days x number of men were added to finish the work in 21 days from beginning. ...

20 men can do a piece of work in 24 days.

After working for 6 days x number of men were

added to finish the work in 21 days from beginning.

Find number of additional men.

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### 2 Answers

Let us say the amount of work done by one man per day is P.

So the amount of work to do `= 20xxPxx24 = 480P`

Work done in six days `= 20xxPxx6 = 120P`

Amount of work left `= 480P-120P = 360P`

If the work to be done in 21 days then we have (21-6) = 15 days left to do the work with additional men.

Let us say we have x number of additional men.

So the amount of men in the team is (20+x). They need to do 360P work in 15 days.

`360P = (20+x)xxPxx15`

`24 = 20+x`

`x = 4`

*So we need 4 additional men to complete the work in 21 days.*

20 men can do a piece of work in 24 days.

So 1 man can do work in 24 x20 days

= 480 days

In 1 day , 1 man can do work =1/480

In 6 days 20 men can do work = 6 x 20 x (1/480)

In (21-6) days (20+x) men can do work= (21-6) x (20+x) x (1/480)

Thus we have

120/(480)+ (15(20+x))/480=1

120+300+15x=480

15x=480-420

15x=60

x=4

Thus number of additional men =4.