Question 1: can do a piece of work in days while can do it in days. How long will they take together to do it?

Answer:

A’s 1 Day

B’s 1 Day work

A’s + B’s 1 Day work =

Therefore both can finish the work in 6 Days.

Question 2: and can do a piece of work in days, days and days respectively. In what time will they all together finish it?

Answer:

A’s 1 Day

B’s 1 Day work

C’s 1 Day work =

(A’s + B’s + C’s) 1 Day work

Therefore all three can finish the work in 4 Days.

Question 3: and together can do a piece of work in days, while alone can do it in days. How long would alone take to do it?

Answer:

A’s 1 Day

B’s 1 Day work

(A’s + B’s) 1 Day work

Solving for Days

Question 4: can do a piece of work in days while can do it in days. With the help of , they finish the work in days. In what time would alone do it?

Answer:

A’s 1 Day

B’s 1 Day work

C’s 1 Day work

(A’s + B’s + C’s) 1 Day work

Solving for Days

Question 5: can do a piece of work in days and alone can do it in days. They worked together on it for days and then left. How long did take to finish the remaining work?

Answer:

A’s 1 Day

B’s 1 Day work

(A’s + B’s) 1 Day work

The amount of work that is completed in 3 days

Amount of work left for B to complete

Therefore the number of days that B will take to finish the work = 9 days

Question 6: can do of a work in days, while can do of the work in days. In how many days can both do it together?

Answer:

If A can do of a work in days, then A can do the entire work in days.

Therefore A’s 1 Day Work

If B can do of a work in days, then B can do the entire work in days.

Therefore B’s 1 Day Work

(A’s + B’s) 1 Day work

Therefore both can do the work in days.

Question 7: can dig a trench in days while can dig it in days. They dug the trench working together and received for it. Find the share of each in it.

Answer:

A’s 1 Day

B’s 1 Day work

Therefore the ratio of work

Therefore A’s share

Therefore B’s share

Question 8: can mow a field in days; can mow it in days while can mow it in days. They all together mowed the field and received for it. How will the money be shared by them?

Answer:

A’s 1 Day

B’s 1 Day work

C’s 1 Day work

Therefore the ratio of their one day’s work

Hence A’s share

Hence A’s share

Hence A’s share

Question 9: and can do a piece of work in days; and in days; and in days. How long will it take them to do the work together? In what time can each finish it, working alone?

Answer:

(A’s + B’s) 1 Day work

(B’s + C’s) 1 Day work

(C’s + D’s) 1 Day work

Adding the above three day work =

Therefore if they all work together, they will take 20 days to finish the work.

Question 10: can do a piece of work in days. He works at it for days and then alone finishes the remaining work in days. In how many days could both do it?

Answer:

A’s 1 Day

Work finished by A in 10 days

B finished the remainder of work in days

Therefore 1 Days work for B

Hence B can do the work in 48 days

(A’s + B’s) 1 Day work

Therefore both can do the work in 30 days.

Question 11: and can together finish a work in days. They worked at it for days and then left. The remaining work was done by alone in more days. In how many days can alone do it?

Answer:

(A’s + B’s) 1 Day work

Amount of work finished by both in 20 days

Work left to be finished

Work done by A in 1 Day

Therefore A can do the work alone in 60 days.

Question 12: can do a certain job in days which alone can do in days. started the work and was joined by after days. In how many days was the whole work completed?

Answer:

A’s 1 Day work

B’s 1 Day work

(A’s + B’s) 1 Day work

Amount of work finished by A in 10 days

Work left to be finished

Days taken by both A and B working together

The work got completed in

Question 13: can do a piece of work in days, while can do in days. They begin together. But, days before the completion of the work, leaves off. Find the total number of days taken to complete the work.

Answer:

A’s 1 Day work

B’s 1 Day work

(A’s + B’s) 1 Day work

Amount of work finished by B in 3 days

Work left to be finished by A and B together

Days taken by A + B working together

The work got completed in

Question 14: is thrice as good a workman as and is twice as good a workman as . All the three took up a job and received as remuneration. Find the share of each.

Answer:

If C takes days to complete the job

Then B will complete the job in days

And A will complete the job in days days

Therefore the ratio of 1 days’ work of

Therefore the share of A Rs.

Therefore the share of B Rs.

Therefore the share of C Rs.

Question 15: can do a certain job in days. is more efficient than . Find the number of days taken by to finish the job.

Answer:

Time taken to finish the job days

A’s 1 Day’s work

B is 60% more efficient

B’s 1 Day’s work

Therefore the number of days B will take to finish the job days

Question 16: is twice as good a workman as and together they finish a piece of work in days. In how many days can alone do it?

Answer:

Let B take days to finish the work.

B’s 1 day’s work

The A will take days to finish the work.

A’s 1 day’s work

(A+B) one day’s work

Solving for

Therefore A will take 21 days to finish the job.

Question 17: Two pipes and can separately fill a tank in minutes and minutes respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?

Answer:

A’s 1 minute fill rate

B’s 1 minute fill rate

A’s and B’s fill rate together

Therefore if A and B are opened simultaneously, the tank will take 20 minutes to fill up.

Question 18: One tap can fill a cistern in hours and the waste pipe can empty the full tank in hours. In what time will the empty cistern be full, if the tap and the waste pipe are kept open together?

Answer:

Tap’s 1 minute fill rate

Waste Pipe’s 1 minute empty rate

Therefore the net fill rate

Therefore if both the tap and the waste pipe are opened simultaneously then it will take hours to fill up.

Question 19: Two pipes and can separately fill a cistern in minutes and minutes respectively , while a third pipe can empty the full cistern in minutes. If all the pipes are opened together, in what time the empty cistern is filled?

Answer:

A’s 1 minute fill rate

B’s 1 minute fill rate

C’s 1 minute empty rate

Therefore the net fill rate

Therefore if all the tap are opened simultaneously then it will take 60 minutes or one hour to fill up.

Question 20: A pipe can fill a tank in hours. Due to a leak in the bottom, it is filled in hours. If the tank is full, how much time will the leak take to empty it?

Answer:

Pipe’s fill rate

Let the leak is at a rate of

Therefore the net fill rate

Solving for hours.

Very Clear; easy to understand.

Q8: C’s 1 day work is 1/8 NOT 1/18. The 3 payment calculations are the ones to do but their results all say 1610 instead of the values: 560, 420, and 630 for A, B, and C respectively.

Thanks for bringing this to my notice. I have corrected the typing error. This is what i call, power of democratization.

Q9: A, B, and C working together will take 20 days NOT 5 days. The answer to the 2nd part of the question (working alone) is missing. A, B, and C will take 120, 40, and 60 days working alone (respectively).

That’s 2 answers in a row wrong – I’m not going to do any more. I suggest anyone reading this moves to a page with correct answers.

Corrected the typing error. Thanks for bringing this up.

thanks

Very easy to understand

Answer of 13 is wrong: See the : 3days before completion of work- which means if A+B both’s worked together the work would have been completed by next 3 days. so when B works alone, the rest of work will take more time: Starting from backward

(A+B) working in 1 day: 5/42 work

in 3 days A+B could have done=(5/42) x 3= 5/14 work which was done by B.

B will finish the work=(5/14) x (21/1)=15/2…………………………………………(a)

Initial A+B work: 9/14 works which would take= (42/5) x (9/14)=27/5 …………………….(b)

Total days taken=(A+B’s days)+ B’s days =(15/2)+(27/5)=129/10

I checked it… seems correct to me. Last three days only B is working.

yes i agrre with mr patra….

I checked and it is right. All it says is that A worked for 3 days in the end alone and the rest of the time A+B worked together. hence the total days is 10 1/2 days. please check once again.

check your solution to Q13. It seems to be incorrect. Please comment on it

let me check