###### Advertisements

###### Advertisements

A and B can do a piece of work in 40 days; B and C in 30 days; and C and A in 24 days.**(i) **How long will it take them to do the work together?**(ii)** In what time can each finish it working alone?

###### Advertisements

#### Solution

A and B can do a piece of work in = 40 days

B and C can do a piece of work in = 30 days

C and A can do a piece of work in = 24 days

(A+B)’s 1-day work =`1/40`

(B+C)’s 1-day work =`1/30`

(C+A)’s 1-day work =`1/24`

**(i)** [(A+B)+(B+C)+(C+A)]’s 1 day work = `1/4+1/30+1/24`

`=(3+4+5)/120`

`=12/120=1/10`

i.e. (A+B+B+C+C+A)'s 1-day work =`1/10`

i.e. 2 (A+B+C)'s 1-day work =`1/10`

∴ (A+B+C)'s 1-day work =`1/10xx1/2`

`=1/20`

∴ (A+B+C) can do the work in = 20 days

**(ii) **A's 1-day work =`1/20-1/30`

`=(3-2)/60=1/60`

∴ A can do the work in 60 days

B's 1-day work =`1/20-1/24`

`=(6-5)/120=1/120`

∴ B can do the work in 120 days

now, C's 1-day work =`1/20-1/40`

`=(2-1)/40=1/40`

C can do the work in 40 days

Hence A can do the work in = 60 days

B can do the work in = 120 days

C can do the work in = 40 days

#### APPEARS IN

#### RELATED QUESTIONS

36 men can do a piece of work in 7 days. How many men will do the same work in 42 days?

In a fort 150 men had provisions for 45 days. After 10 days, 25 men left the fort. How long would the food last at the same rate?

72 men do a piece of work in 25 days. In how many days will 30 men do the same work?

In order to complete a work in 28 days, 60 men are required. How many men will be required if the same work is to be completed in 40 days?

A fort had provisions for 450 soldiers for 40 days. After 10 days, 90 more soldiers come to the fort. Find in how many days will the remaining provisions last at the same rate?

A contractor undertakes to dig a canal, 6 kilometers long, in 35 days and employed 90 men. He finds that after 20 days only 2 km of the canal has been completed. How many more men must be employed to finish the work on time?

A and B together can do a piece of work in `6 2/3` days, but B alone can do it in 10 days. How long will A take to do it alone?

A can do a piece of work in 10 days; B in 18 days; and A, B, and C together in 4 days. In what time would C alone do it?

A and B can do a work in 8 days; B and C in 12 days, and A and C in 16 days. In what time could they do it, all working together?

A can do a piece of work in 10 days, B in 12 days, and C in 15 days. All begin together but A leaves the work after 2 days and B leaves 3 days before the work is finished. How long did the work last?

P and Q can do a piece of work in 12 days and 15 days respectively. P started the work alone and then after 3 days, Q joined him till the work was completed. How long did the work last?

P alone can do `1/2` of a work in 6 days and Q alone can do `2/3` of the same work in 4 days. in how many days will they finish `3/4` of the work, working together?

X alone can do a piece of work in 6 days and Y alone in 8 days. X and Y undertook the work for ₹ 48000. With the help of Z, they completed the work in 3 days. How much is Z’s share?