ICSE Board: Suggested Books ICSE Board: Foundation Mathematics Class 8: Reference Books Class 8: NTSE Preparation --------------------------------------------------------------

Q1. A can do a piece of work in 15 days while B can do it in 10 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.

Q2. A, B and C can do a piece of work in 12 days, 15 days and 10 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.

Q3. A and B together can do a piece of work in 35 days, while A alone can do it in 60 days. How long would B alone take to do it?

Answer:

A’s 1 Day =

B’s 1 Day work =

(A’s + B’s) 1 Day work =

Solving for = 84 Days

Q4. A can do a piece of work in 20 days while B can do it in 15 days. With the help of C, they finish the work in 5 days. In what time would C 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 = 12 Days

Q5. A can do a piece of work in 12 days and B alone can do it in 16 days. They worked together on it for 3 days and then A left. How long did B 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

Q6. A can do of a work in 5 days, while B can do of the work in 6 days. In how many days can both do it together?

Answer:

If A can do of a work in 5 days, then A can do the entire work in 20 days.

Therefore A’s 1 Day Work =

If B can do of a work in 6 days, then B can do the entire work in 30 days.

Therefore B’s 1 Day Work =

(A’s + B’s) 1 Day work =

Therefore both can do the work in 12 days.

Q7. A can dig a trench in 6 days while B can dig it in 8 days. They dug the trench working together and received 1120 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 =

Q8. A can mow a field in 9 days; B can mow it in 12 days while C can mow it in 8 days. They all together mowed the field and received 1610 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 =

Q9. A and B can do a piece of work in 30 days; B and C in 24 days; C and A in 40 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.

Q10. A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 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 42 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.

Q11. A and B can together finish a work in 30 days. They worked at it for 20 days and then B left. The remaining work was done by A alone in 20 more days. In how many days can A 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.

Q12. A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 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

Q13. A can do a piece of work in 14 days, while B can do in 21 days. They begin together. But, 3 days before the completion of the work, A 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

Q14. A is thrice as good a workman as B and B is twice as good a workman as C. All the three took up a job and received 1800 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.

Q15. A can do a certain job in 12 days. B is 60% more efficient than A. Find the number of days taken by B to finish the job.

Answer:

Time taken to finish the job = 12 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

Q16. A is twice as good a workman as B and together they finish a piece of work in 14 days. In how many days can A 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.

Q17. Two pipes A and B can separately fill a tank in 36 minutes and 45 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.

Q18. One tap can fill a cistern in 3 hours and the waste pipe can empty the full tank in 5 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.

Q19. Two pipes A and B can separately fill a cistern in 20 minutes and 30 minutes respectively , while a third pipe C can empty the full cistern in 15 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.

Q20. A pipe can fill a tank in 16 hours. Due to a leak in the bottom, it is filled in 24 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.

ICSE Board: Suggested Books ICSE Board: Foundation Mathematics Class 8: Reference Books Class 8: NTSE Preparation --------------------------------------------------------------

Very Clear; easy to understand.

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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.

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

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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.

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Corrected the typing error. Thanks for bringing this up.

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