RS Aggarwal solution class 8 chapter 13 Time and Work Test Paper 13

Test Paper 13

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Q1 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 1:

A can do a piece of work in 10 days while B alone can do it in 15 days. In how many days can both finish the same work?

Answer 1:

A can do a piece of work in 10 days.A's 1 day work = 110B can do a piece of work in 15 days.B's 1 day work =115(A+B)'s 1 day work = 110+115=3+230=530=16A and B working together can complete the work in 6 days.

Q2 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 2:

A and B can do a piece of work in 15 days; B and C in 12 days; C and A in 20 days. How many days will be taken by A, B and C working together to finish the work?

Answer 2:

(A+B) can do a work in 15 days. (A+B)'s 1 day work = 115(B+C) can do a work in 12 days. (B+C)'s 1 day work = 112(C+A) can do a work in 20 days. (C+A)'s 1 day work = 1202(A+B+C)'s 1 day work =115+112+120=4+5+360=1260=15(A+B+C)'s 1 day work = 110A, B and C working together require 10 days to complete the work.


Q3 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 3:

Tap A can fill a cistern in 8 hours and tap B can empty it in 12 hours. How long will it take to fill the cistern if both of them are opened together?

Answer 3:

Tap A can fill a cistern in 8 hours.Part of cistern filled by Tap A in 1 hour= 18Tap B empties the cistern in 12 hours.Part of cistern emptied by Tap B in 1 hour = -112(negative sign shows that tap B drains the tank)Part of cistern filled in one hour when both taps are opened together = 18-112 = 3-224 = 124Therefore, it will take 24 hours to fill the cistern.


Q4 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 4:

2 men or 3 women can do a piece of work in 16 days. In how many days can 4 men and 6 women do the same work?

Answer 4:

Work of 2 men = Work of 3 womenWork of 1 man = 32womenThree women can do a piece of work in 16 days.As 4 men and 6 women = (4×32) women + 6 women = 6 women + 6 women = 12 womenAlso, 3 women can do the work in 16 days.So, work done by 3 women in one day = 116∴ Work done by 1 woman in one day = 148 Work done by 12 women in one day = 14Thus, 4 men and 6 women will complete the work in 4 days.

Q5 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 5:

A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak?

Answer 5:

Time taken by the pipe to fill the cistern = 9 hoursPart of the cistern filled in one hour = 19Suppose the leak empties the full cistern in x hours.Part of the cistern emptied in one hour = -1x(negative sign implies a leak)Time taken by the cistern to fill completely due to the leak = 10 hoursPart of the cistern filled in one hour due to the leak = 110  110=19-1x 1x=19-110=190x = 90 hoursTherefore, the leak will empty a full cistern in 90 hours.


Q6 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 6:

Mark (✓) against the correct answer:
The rates of working of two tapes A and B are in the ratio 2 : 3. The ratio of the time taken by A and B respectively to fill a given cistern is
(a) 2 : 3
(b) 3 : 2
(c) 4 : 9
(d) 9 : 4

Answer 6:

(b) 3:2

Rates at which taps A and B work = 2:3The ratio of time taken by taps A and B to fill the cistern = 1Rates at which taps A and B work = 123 = 32 = 3:2


Q7 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 7:

Mark (✓) against the correct answer:
A can finish a piece of work in 12 hours while B can finish it in 15 hours. How long will both take to finish it, working together?
(a) 9 hours
(b) 623 hours
(c) 634 hours
(d) 813 hours

Answer 7:

(b) 623 hours

A's 1 hour work = 112B's 1 hour work = 115(A+B)'s 1 hour work = 112+115=960 = 320Time taken by A and B to complete the work together = 203= 623hours


Q7 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 8:

Mark (✓) against the correct answer:
A can do a piece of work in 14 days and B is 40% more efficient than A. In how many days can B finish it?
(a) 10 days
(b) 712 days
(c) 514 days
(d) 535 days

Answer 8:

(a) 10 days
A's 1 day work = 114B is 40%more efficient than A. B's 1 day work = 140100×114=110B takes 10 days to complete the work.

Q9 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 9:

Mark (✓) against the correct answer:
A pump can fill a cistern in 2 hours. Due to a leak in the tank it takes 213 hours to fill it. The leak can empty the full tank in
(a) 7 hours
(b) 14 hours
(c) 8 hours
(d) 3 hours

Answer 9:

(b) 14 hours

A pump fills a tank in 2 hours.Part of tank filled by the pump in one hour = 12Let x hours be the time required for water to leak from the cistern.Part of tank drained by the leak in one hour =- 1xTime required to fill the leaking cistern = 213=73hoursPart of tank stored with water in one hour = 3737=12-1x1x=12-37=7-614=114x =14 hours


Q10 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 10:

Mark (✓) against the correct answer:
A works twice as fast as B. If both of them can together finish a peice of work in 12 hours, then B alone can do it in
(a) 24 hours
(b) 27 hours
(c) 36 hours
(d) 18 hours

Answer 10:

(c) 36 hours

Suppose B takes x hours to complete the work. B's 1 hour work = 1xA works twice as fast as B. A's 1 hour work = 2x112 = 1x+2x = 3xx = 36 hours


Q11 | Test Paper 13 | Class 8 | RS AGGARWAL | chapter 13 | Time and Work

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Question 11:

Fill in the blanks.
(i) A tap can fill a tank in 6 hours. The part of the tank filled in 1 hour is .........
(ii) A and B working together can finish a piece of work in 6 hours while A alone can do it in 9 hours. B alone can do it in ......... hours.
(iii) A can do a work in 16 hours and B alone can do it in 24 hours. If A, B and C working together can finish it in 8 hours, then C alone can finish it in ......... hours.
(iv) If A's one day's work is 320, then A can finish the whole work in ......... days.

Answer 11:

(i) A tap can fill a tank in 6 hours. In 1 hour, 16 of the tank is filled.

(ii) 18 hours
(A+B)'s 1 hour work =16A's 1 hour work =19B's 1 hour work = 16-19=3-218=118Thus, B takes 18 hours to finish the work.


(iii) 48 hours
A' s 1 hour work = 116B's 1 hour work = 124C's 1 hour work = 1x(A+B+C)'s 1 hour work = 18Therefore, 1x=18-116-124=6-3-248=148or, x = 48 hoursThus, C alone takes 48 hours to complete the work.

(iv) The time for completion is the reciprocal of the work done in one day. Therefore, A can complete the whole work in 203= 623 days

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