###### Advertisements

###### Advertisements

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?

###### Advertisements

#### Solution

A and B can do a work in = 8 days

B and C can do a work in = 12 days

A and C can do a work in = 16 days

(A+B)’s 1-day work =`1/8`

(B+C)’s 1-day work =`1/12`

(A+C)'s 1-day work =`1/16`

∴ [(A+B)+(B+C)+(A+C)]'s 1 day work

`=1/8+1/12+1/16`

i.e. [A+B+B+C+A+C]'s 1 day work

`=1/8+1/12+1/16`

`=(6+4+3)/48=13/48`

i.e. 2(A+B+C)'s 1-day work =`13/48`

i.e. (A+B+C)'s 1-day work =`13/48xx1/2=13/96`

∴ (A+B+C) can do the work in =`96/13`days

`=7 5/13` days

#### APPEARS IN

#### RELATED QUESTIONS

22 men can dig a 27 m long trench in one day. How many men should be employed for digging 135 m long trench of the same type in one day?

12 pipes, all of the same size, fill a tank in 42 minutes. How long will it take to fill the same tank, if 21 pipes of the same size are used?

If 3 men or 6 boys can finish a work in 20 days, how long will 4 men and 12 boys take to finish the same work?

90 men can complete a work in 24 days working 8 hours a day. How many men are required to complete the same work in 18 days working `7 1/2` hours a day?

Twelve typists, all working with the same speed, type a certain number of pages in 18 days working 8 hours a day. Find, how many hours per day must sixteen typists work in order to type the same number of pages in 9 days?

A can do a piece of work in 10 days and B in 15 days. How long will they take together to finish it?

A can do a work in 15 days and B in 20 days. If they together work on it for 4 days; what fraction of the work will be left?

A, B, and C can do a piece of work in 6 days, 12 days, and 24 days respectively. In what time will they altogether do it?

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 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?

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?