- 20 men complete one-third of a piece of work in 20 days.

- More men needed to finish the rest of work in 25 more days can be figure out in this way.

## Explanation

Three given entities here are

- Work
- Days
- Men

To determine the relation here, let suppose; Men needed to finish the rest of work in 25 more days = y

__Case I__

20 men complete work in 20 days = 1/3

Remaining work = 2/3

Work Men

1/3Â Â Â Â Â Â Â Â Â Â Â Â Â 20

2/3Â Â Â Â Â Â Â Â Â Â Â y

- More work mean more men.
- Less work mean less men.

This clearly indicates that there is direct relation.

Direct/Indirect relation tells how the equation will be written.

1/3 : 2/3 :: 20 : y ________ (i)

__Case II__

Days Men

20Â Â Â Â Â Â Â Â Â Â Â Â Â Â 20

25Â Â Â Â Â Â Â Â Â Â Â Â y

- More days mean less men.
- Less days mean more men.

This clearly indicates that there is inverse relation.

Direct/Indirect relation tells how the equation will be written.

25 : 20 :: 20 : y ________ (ii)

By (i) and (ii)

1/3 : 2/3 :: 20 : y

25 : 20

1/3 x 25 x y = 2/3 x 20 x 20 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 32) and more men = 32 â€“ 20 = 12 men

## To Find

More men needed to finish the rest of work in 25 more days = ?

## Solution

__Method I__

Let suppose

Men needed to finish the rest of work in 25 more days = y

Work Days Men

1/3Â Â Â Â Â Â Â Â Â Â Â Â Â 20Â Â Â Â Â Â Â Â Â Â Â Â Â Â 20

2/3 Â Â Â Â Â Â Â Â Â Â Â Â 25 Â Â Â Â Â Â Â Â Â Â Â y

- Relation between work and men is direct.
- Relation between days and men is inverse.

So

1/3 : 2/3 :: 20 : y

25 : 20

1/3 x 25 x y = 2/3 x 20 x 20

25y = 2 x 20 x 20

y = 2 x 4 x 4

y = 2 x 16

y = 32

Men needed to finish the rest of work in 25 more days = 32 men

More men needed to finish the rest of work in 25 more days = 32 â€“ 20

**More men needed to finish the rest of work in 25 more days = 12 men answer**

__Method II__

Men needed to finish one-third of a work in 20 days = 20 men

Men needed to finish one-third of a work in 1 day = (20 x 20) men

Men needed to finish one-third of a work in 1 day = 400 men

Men needed to finish entire work in 1 day = (400 x 3) men

Men needed to finish entire work in 1 day = 1200 men

Men need to finish entire work in 25 days = 1200/25 men

Men needed to finish entire work in 25 days = 48 men

Men needed to finish 2/3 of work in 25 days = (48 x 2/3) men

Men needed to finish 2/3 of work in 25 days = 32 men

Men needed to finish the rest of work in 25 more days = 32 men

More men needed to finish the rest of work in 25 more days = 32 â€“ 20

**More men needed to finish the rest of work in 25 more days = 12 men answer**

### Conclusion

20 men complete one-third of a piece of work in 20 days. 12 more men should be employed to finish the rest of work in 25 more days.