- If 3 men or 6 boys can do a piece of work in 10 days working 7 hours a day.

- Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large can be figure out in this way.

## Explanation

Three given entities here are

- Boys
- Hours
- Days

To determine the relation here, let suppose; days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work = y

__Case I__

As

3 men = 6 boys

1 man = 2 boys

6 men = 12 boys

6 men and 2 boys = 14 boys

BoysÂ Â Â Â Â Â Â Â Â Days

6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10

14Â Â Â Â Â Â Â Â Â Â Â Â Â y

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

This clearly indicates that there is inverse relation.

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

14 : 6 :: 10 : y ________ (i)

__Case II__

Hours Days

7Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10

8Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â y

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

This clearly indicates that there is inverse relation.

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

8 : 7 :: 10 : y ________ (ii)

By (i) and (ii)

14 : 6 :: 10 : y

8 : 7

14 x 8 x y = 6 x 7 x 10 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 7.5 days)

## To Find

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = ?

## Solution

__Method I__

__Method I__

Let suppose

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work = y

Boys Hours Days

6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 7Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10

14Â Â Â Â Â Â Â Â Â Â Â Â 8Â Â Â Â Â Â Â Â Â Â Â Â Â y

- Relation between boys and days is inverse.
- Relation between hours and days is also inverse.

So

14 : 6 :: 10 : y

8 : 7

14 x 8 x y = 6 x 7 x 10

112y = 420

y = 420/112

y = 3.75 days

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work = 3.75 days

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = (3.75 x 2) days

**Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = 7.5 days**

__Method II__

As

3 men = 6 boys

1 man = 2 boys

6 men = 12 boys

6 men and 2 boys = 14 boys

Days required by 6 boys working for 7 hours a day to complete a piece of work** = **10 days

Days required by 6 boys working for 1 hour a day to complete a piece of work** = **(10 x 7) days

Days required by 6 boys working for 1 hour a day to complete a piece of work** = **70 days

Days required by 1 boy working for 1 hour a day to complete a piece of work** = **(70 x 6) days

Days required by 1 boy working for 1 hour a day to complete a piece of work** = **420 days

Days required by 1 boy working for 8 hours a day to complete a piece of work** = **420/8 days

Days required by 1 boy working for 8 hours a day to complete a piece of work** = **52.5 days

Days required by 14 boys working for 8 hours a day to complete a piece of work** = **52.5/14 days

Days required by 14 boys working for 8 hours a day to complete a piece of work** = **3.75 days

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = (3.75 x 2) days

**Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = 7.5 days**

## Conclusion

If 3 men or 6 boys can do a piece of work in 10 days working 7 hours a day; 7.5 days it will take to complete a piece of work twice as large with 6 men and 2 boys working together for 8 hours a day.