myhelper: 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:

$A can do a piece of work in 10 days . A' s 1 day work = \frac{1}{10} B can do a piece of work in 15 days . B' s 1 day work = \frac{1}{15} (A + B)' s 1 day work = \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{5}{30} = \frac{1}{6} A and B working together can complete the work in 6 days .$

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:

$(A + B) can do a work in 15 days . ∴ (A + B)' s 1 day work = \frac{1}{15} (B + C) can do a work in 12 days . ∴ (B + C)' s 1 day work = \frac{1}{12} (C + A) can do a work in 20 days . ∴ (C + A)' s 1 day work = \frac{1}{20} 2 (A + B + C)' s 1 day work = \frac{1}{15} + \frac{1}{12} + \frac{1}{20} = \frac{4 + 5 + 3}{60} = \frac{12}{60} = \frac{1}{5} (A + B + C)' s 1 day work = \frac{1}{10} A, B and C working together require 10 days to complete the work .$

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:

$Tap A can fill a cistern in 8 hours . Part of cistern filled by Tap A in 1 hour = \frac{1}{8} Tap B empties the cistern in 12 hours . Part of cistern emptied by Tap B in 1 hour = - \frac{1}{12} (negative sign shows that tap B drains the tank) Part of cistern filled in one hour when both taps are opened together = \frac{1}{8} - \frac{1}{12} = \frac{3 - 2}{24} = \frac{1}{24} Therefore, it will take 24 hours to fill the cistern .$

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:

$Work of 2 men = Work of 3 women \Rightarrow Work of 1 man = \frac{3}{2} women Three women can do a piece of work in 16 days . As 4 men and 6 women = (4 \times \frac{3}{2}) women + 6 women = 6 women + 6 women = 12 women Also, 3 women can do the work in 16 days . So, work done by 3 women in one day = \frac{1}{16} ∴ Work done by 1 woman in one day = \frac{1}{48} \Rightarrow Work done by 12 women in one day = \frac{1}{4} Thus, 4 men and 6 women will complete the work in 4 days .$

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:

$Time taken by the pipe to fill the cistern = 9 hours Part of the cistern filled in one hour = \frac{1}{9} Suppose the leak empties the full cistern in x hours . Part of the cistern emptied in one hour = - \frac{1}{x} (negative sign implies a leak) Time taken by the cistern to fill completely due to the leak = 10 hours Part of the cistern filled in one hour due to the leak = \frac{1}{10} ∴ \frac{1}{10} = \frac{1}{9} - \frac{1}{x} \Rightarrow \frac{1}{x} = \frac{1}{9} - \frac{1}{10} = \frac{1}{90} x = 90 hours Therefore, the leak will empty a full cistern in 90 hours .$

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

$Rates at which taps A and B work = 2 : 3 The ratio of time taken by taps A and B to fill the cistern = \frac{1}{Rates at which taps A and B work} = \frac{1}{\frac{2}{3}} = \frac{3}{2} = 3 : 2$

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) $6 \frac{2}{3}$ hours
(c) $6 \frac{3}{4}$ hours
(d) $8 \frac{1}{3}$ hours

Answer 7:

(b) $6 \frac{2}{3} h o u r s$

$A' s 1 hour work = \frac{1}{12} B' s 1 hour work = \frac{1}{15} (A + B)' s 1 hour work = \frac{1}{12} + \frac{1}{15} = \frac{9}{60} = \frac{3}{20} Time taken by A and B to complete the work together = \frac{20}{3} = 6 \frac{2}{3} hours$

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) $7 \frac{1}{2}$ days
(c) $5 \frac{1}{4}$ days
(d) $5 \frac{3}{5}$ days

Answer 8:

(a) 10 days
$A' s 1 day work = \frac{1}{14} B is 40 % more efficient than A . ∴ B' s 1 day work = \frac{140}{100} \times \frac{1}{14} = \frac{1}{10} B takes 10 days to complete the work .$

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 $2 \frac{1}{3}$ 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

$A pump fills a tank in 2 hours . Part of tank filled by the pump in one hour = \frac{1}{2} Let x hours be the time required for water to leak from the cistern . Part of tank drained by the leak in one hour = - \frac{1}{x} Time required to fill the leaking cistern = 2 \frac{1}{3} = \frac{7}{3} hours Part of tank stored with water in one hour = \frac{3}{7} \Rightarrow \frac{3}{7} = \frac{1}{2} - \frac{1}{x} \frac{1}{x} = \frac{1}{2} - \frac{3}{7} = \frac{7 - 6}{14} = \frac{1}{14} x = 14 hours$

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

$Suppose B take s x hour s to complete the work . ∴ B' s 1 hour work = \frac{1}{x} A works twice as fast as B . ∴ A's 1 hour work = \frac{2}{x} \frac{1}{12} = \frac{1}{x} + \frac{2}{x} = \frac{3}{x} \Rightarrow x = 36 hours$

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 $\frac{3}{20}$ , then A can finish the whole work in ......... days.

Answer 11:

(i) A tap can fill a tank in 6 hours. In 1 hour, $\frac{1}{6}$ of the tank is filled.

(ii) 18 hours
$(A + B)' s 1 hour work = \frac{1}{6} A' s 1 hour work = \frac{1}{9} B' s 1 hour work = \frac{1}{6} - \frac{1}{9} = \frac{3 - 2}{18} = \frac{1}{18} Thus, B takes 18 hours to finish the work .$

(iii) 48 hours
$A' s 1 hour work = \frac{1}{16} B' s 1 hour work = \frac{1}{24} C' s 1 hour work = \frac{1}{x} (A + B + C)' s 1 hour work = \frac{1}{8} Therefore, \frac{1}{x} = \frac{1}{8} - \frac{1}{16} - \frac{1}{24} = \frac{6 - 3 - 2}{48} = \frac{1}{48} or, x = 48 hours Thus, C alone takes 48 hours to complete the wor k .$

(iv) The time for completion is the reciprocal of the work done in one day. Therefore, A can complete the whole work in $\frac{20}{3} = 6 \frac{2}{3} days$

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

Test Paper 13

Page-176

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

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Question 1:

Answer 1:

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

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Question 2:

Answer 2:

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

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Question 3:

Answer 3:

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

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Answer 4:

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

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

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Answer 6:

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

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

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

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

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Answer 10:

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

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