- 2 men and 7 boys can do a piece of work in 14 days.

- 3 men and 8 boys can do the same in 11 days.

- Days required by 8 men and 6 boys to do three times the amount of this work can be figure out as in this way.

## Explanation

Let suppose

- Work done by 1 man in 1 day = y

- Work done by 1 boy in 1 day = z

According to the First given condition

2y + 7z = 1/14 ________ (i)

According to second given condition

3y + 8z = 1/11 ________ (ii)

By solving equation (i) and (ii) simultaneously, we can easily figure out the value of y and z which further leads to determine the days required by 8 men and 6 boys to finish three times the amount of this work.

## To Find

Days required by 8 men and 6 boys to finish three times the amount of this work = ?

## Solution

Let suppose

- Work done by 1 man in 1 day = y

- Work done by 1 boy in 1 day = z

According to the First given condition

2y + 7z = 1/14 ________ (i)

According to second given condition

3y + 8z = 1/11 ________ (ii)

Multiplying equation (i) with 3 and equation (ii) with 2 and subtracting from equation (i)

(6y + 21z) – (6y + 16z) = 3/14 – 2/11

6y + 21z – 6y – 16z = (33 – 28)/154

5z = 5/154

770z = 5

z = 5/770

z = 1/154

Work done by 1 boy in 1 day = 1/154

Work done by 6 boys in 1 day = 6/154

Putting (z = 1/154) in equation (i)

2y + 7(1/154) = 1/14

2y + 1/22 = 1/14

28y + 7/11 = 1

308y + 7 = 11

308y = 4

y = 4/308

y = 1/77

Work done by 1 man in 1 day = 1/77

Work done by 8 men in 1 day = 8/77

Work done by 8 men and 6 boys in 1 day = 8/77 + 6/154

Work done by 8 men and 6 boys in 1 day = (16 + 6)/154

Work done by 8 men and 6 boys in 1 day = 22/154

Work done by 8 men and 6 boys in 1 day = 1/7

Days required by 8 men and 6 boys to finish the work = 7 days

Days required by 8 men and 6 boys to finish three times the amount of this work = (7 x 3) days

**Days required by 8 men and 6 boys to finish three times the amount of this work = 21 days**

## Conclusion

2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in 21 days.