myhelper: RS Aggarwal solution class 8 chapter 13 Time and Work Exercise 13B

Exercise 13B

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Q1 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 1:

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A alone can do a piece of work in 10 days and B alone can do it in 15 days. In how many days will A and B together do the same work?
(a) 5 days
(b) 6 days
(c) 8 days
(d) 9 days

Answer 1:

(b) 6 days

$A can do a work in 10 days . A' s 1 day work = \frac{1}{10} B can do a work in 15 days . B' s 1 day work = \frac{1}{15} (A + B)' s 1 day work = \frac{1}{10} + \frac{1}{15} = \frac{5}{30} = \frac{1}{6} A and B together will take 6 days to complete the work .$

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Question 2:

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A man can do a piece of work in 5 days. He and his son working together can finish it in 3 days. In how many days can the son do it alone?
(a) $6 \frac{1}{2}$ days
(b) 7 days
(c) $7 \frac{1}{2}$ days
(d) 8 days

Answer 2:

(c) $7 \frac{1}{2} d a y s$

$A man can do a work in 5 days . The man' s 1 day work = \frac{1}{5} The man and the son can do the work in 3 days . The man and his son' s 1 day work = \frac{1}{3} Let the son' s 1 day work be \frac{1}{x} . Therefore, \frac{1}{3} = \frac{1}{5} + \frac{1}{x} or, \frac{1}{x} = \frac{1}{3} - \frac{1}{5} = \frac{5 - 3}{15} = \frac{2}{15} x = \frac{15}{2} = 7 \frac{1}{2} days$

Q3 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 3:

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A can do a job in 16 days and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in
(a) 34 days
(b) 22 days
(c) 36 dyas
(d) 48 days

Answer 3:

(d) 48 days

$A can do a job in 16 days . B can do the job in 12 days . Suppose C can do the job in x days . A' s 1 day work = \frac{1}{16} B' s 1 day work = \frac{1}{12} C' s 1 day work = \frac{1}{x} A, B and C together can complete the work in 6 days . (A + B + C)' s 1 day work = \frac{1}{6} Therefore, \frac{1}{6} = \frac{1}{16} + \frac{1}{12} + \frac{1}{x} \Rightarrow \frac{1}{x} = \frac{1}{6} - \frac{1}{16} - \frac{1}{12} = \frac{8 - 3 - 4}{48} = \frac{1}{48} x = 48 Therefore, C alone can complete the job in 48 days .$

Q4 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 4:

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To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
(a) 30 days
(b) 35 days
(c) 40 days
(d) 45 days

Answer 4:

(a) 30 days

$L e t B t a k e x d a y s t o c o m p l e t e t h e w o r k . T h e n A t a k e s (x + \frac{50}{100} x) = 1.5 x A' s 1 d a y' s w o r k = \frac{1}{1.5 x} = \frac{2}{3 x} B' s 1 d a y' s w o r k = \frac{1}{x} (A + B) t a k e s 18 d a y s t o c o m p l e t e t h e w o r k . (A + B)' s 1 d a y' s n e t w o r k = \frac{1}{18} o r \frac{1}{18} = \frac{2}{3 x} + \frac{1}{x} \Rightarrow \frac{1}{18} = \frac{5}{3 x} B y c r o s s - m u l t i p l i c a t i o n, w e g e t : x = 30 d a y s ∴ B a l o n e w i l l t a k e 30 d a y s t o c o m p l e t e t h e w o r k .$

Q5 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 5:

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A works twice as fast as B. If both of them can together finish a piece of work in 12 days, then B alone can do it in
(a) 24 days
(b) 27 days
(c) 36 days
(d) 48 days

Answer 5:

$Then B takes 2 x days to complete the work .$

$A' s 1 day' s work = \frac{1}{x} B' s 1 day' s work = \frac{1}{2 x} A and B take 12 days to complete the work .$

$Net work done by (A + B) in 1 day = \frac{1}{12} = \frac{1}{x} + \frac{1}{2 x} = \frac{3}{2 x} \Rightarrow 2 x = 36 \Rightarrow x = 18 A can complete the work by himself in 18 days .$

$B will take 36 days, i . e ., twice as long as the time taken by A .$

Q6 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 6:

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A alone can finish a piece of work in 10 days which B alone can do in 15 days. If they work together and finish it, then out of total wages of Rs 3000, A will get
(a) Rs 1200
(b) Rs 1500
(c) Rs 1800
(d) Rs 2000

Answer 6:

(c) Rs. 1800

Since the wage distribution will follow the work distribution ratio, we have:

Work done by A in 1 day $= \frac{1}{10}$
Work done by B in 1 day $= \frac{1}{15}$

Net work done by (A+B) in 1 day $= \frac{1}{10} + \frac{1}{15} = \frac{5}{30} = \frac{1}{6}$

i.e., (A+B) will take 6 days to complete the work.

A's share of work in a day = $\frac{1}{10} \div \frac{1}{6} = \frac{1}{10} \times \frac{6}{1} = \frac{6}{10} = \frac{3}{5}$

∴ A's wage = $\frac{3}{5} \times 3000 = Rs 1800$

Q7 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 7:

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The rates of working of A and B are in the ratio 3 : 4. The number of days taken by them to finish the work are in the ratio
(a) 3 : 4
(b) 9 : 16
(c) 4 : 3
(d) 16 : 9

Answer 7:

(c) 4:3

The number of days taken for working is the reciprocal of the rate of work.

$i . e ., number of days taken = \frac{1}{rate of work} = \frac{1}{\frac{3}{4}} = \frac{4}{3}$

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Question 8:

Tick (✓) the correct answer:
A and B together can do a piece of work in 12 days; B and C can do it in 20 days while C and A can do it in 15 days. A, B and C all working together can do it in
(a) 6 days
(b) 9 days
(c) 10 days
(d) $10 \frac{1}{2}$ days

Answer 8:

(c) 10 days

$(A + B) can do a work in 12 days . (B + C) can do a work in 20 days . (C + A) can do a work in 15 days . Now, we have : Work done by (A + B) in 1 day = \frac{1}{12} Work done by (B + C) in 1 day = \frac{1}{20} Work done by (C + A) in 1 day = \frac{1}{15} Net work done by 2 (A + B + C) = \frac{1}{12} + \frac{1}{20} + \frac{1}{15} = \frac{5 + 3 + 4}{60} = \frac{12}{60} = \frac{1}{5} Net work done by (A + B + C) in 1 day = \frac{1}{10} ∴ If A, B and C work together, they will complete the work in 10 days .$

Q9 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 9:

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3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to do it?
(a) 6 days
(b) 5 days
(c) 4 days
(d) 3 days

Answer 9:

(c) 4 days

$Three men can complete the work in 12 days . Thus, one man can complete the work in 36 days . Rate of work done by one man in 1 day = \frac{1}{36} Similarly, rate of work done by one woman in 1 day = \frac{1}{5 \times 12} = \frac{1}{60} Now, six men will do \frac{6}{36}, i . e ., \frac{1}{6} unit of work in a day . Five women will do \frac{5}{60}, i, e ., \frac{1}{12} unit of work in a day . ∴ Total work done in 1 day = \frac{1}{6} + \frac{1}{12} = \frac{1}{4} unit$

$Thus, six men and five women will take 4 days to complete the work .$

The work can be completed in 4 days.

Q10 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 10:

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A can do a piece of work in 15 days. B is 50% more efficient than A. B can finish it in
(a) 10 days
(b) $7 \frac{1}{2}$ days
(c) 12 days
(d) $10 \frac{1}{2}$ days

Answer 10:

(a) 10 days

$Work done by A in 1 day = \frac{1}{15} B is 50 % more efficient than A . ∴ Work done by B in 1 day = \frac{150}{100} \times \frac{1}{15} = \frac{1}{10} Thus, B can complete the work in 10 days .$

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Q11 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 11:

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A does 20% less work than B. If A can finish a piece of work in $7 \frac{1}{2}$ hours, then B can finish it in
(a) 5 hours
(b) $5 \frac{1}{2}$ hours
(c) 6 hours
(d) $6 \frac{1}{2}$ hours

Answer 11:

(c) 6 hours

$Time taken by A to finish the piece of work = 7 \frac{1}{2} hours = \frac{15}{2} hours Work done by A in 1 hour = \frac{2}{15} Let B take x hours to finish the work . Work done by B in 1 hours = \frac{1}{x} A can work 20 % less than B, or A can do \frac{4}{5} of B' s work .$

$Now, \frac{(\frac{4}{5})}{1} = \frac{(\frac{2}{15})}{(\frac{1}{x})} \Rightarrow \frac{4}{5} = \frac{2 x}{15} \Rightarrow x = \frac{15 \times 4}{5 \times 2} = 6 hours$

Q12 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 12:

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A can do a piece of work in 20 days which B alone can do in 12 days. B worked at it for 9 days. A can finish the remaining work in
(a) 3 days
(b) 5 days
(c) 7 days
(d) 11 days

Answer 12:

(b) 5 days

$A can complete the work in 20 days . Work done by A in 1 day = \frac{1}{20} B can complete the work in 12 days . Work done by B in 1 day = \frac{1}{12} In 9 days, B completes \frac{9}{12}, i . e ., \frac{3}{4} of the work and leaves 1 - \frac{3}{4}, i . e ., \frac{1}{4} of the work undone . ∴ Time taken by A = \frac{1}{4} \div \frac{1}{20} = \frac{1}{4} \times 20 = 5 days$

Q13 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 13:

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A can do a piece of work in 25 days, which B alone can do in 20 days. A started the work and was joined by B after 10 days. The work lasted for
(a) $12 \frac{1}{2}$ days
(b) 15 days
(c) $16 \frac{2}{3}$ days
(d) 14 days

Answer 13:

$Work done by A in 1 day = \frac{1}{25} B can do the same work in 20 days .$

$Work done by B in 1 day = \frac{1}{20} A alone completes \frac{10}{25}, i, e ., \frac{2}{5} of the work in 10 days .$

$Now, work remaining = 1 - \frac{2}{5} = \frac{3}{5}$

$Work done by (A + B) in 1 day = \frac{1}{25} + \frac{1}{20} = \frac{9}{100}$

∴ Time taken if they work together=35÷9100=35×1009=203=623 days

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Question 14:

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Two pipes can fill a tank in 20 minutes and 30 minutes respectively. If both the pipes are opened simultaneously, then the tank will be filled in
(a) 10 minutes
(b) 12 minutes
(c) 15 minutes
(d) 25 minutes

Answer 14:

(b) 12 minutes

$First pipe can fill a tank in 20 minutes .$

$Second pipe can fill the tank in 30 minutes .$

$Part of tank filled by the first pipe in one minute = \frac{1}{20}$

$P art of tank filled by the second pipe in one minute \frac{1}{30}$

$Part of tank filled by both pipes in one minute = \frac{1}{20} + \frac{1}{30} = \frac{5}{60} = \frac{1}{12}$

$Thus, it takes 12 minutes to fill the tank using both the pipes.$

Q15 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 15:

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A tap can fill a cistern in 8 hours and another tap can empty the full cistern in 16 hours. If both the taps are open, the time taken to fill the cistern is
(a) $5 \frac{1}{3}$ hours
(b) 10 hours
(c) 16 hours
(d) 20 hours

Answer 15:

(c) 16 hours

$A tap can fill a cistern in 8 hours . Part of cistern filled in one hour = \frac{1}{8} A tap can empty the cistern in 16 hours . Part of cistern emptied in one hour = - \frac{1}{16} (negative sign shows that the cistern is being drained) ∴ Part of cistern filled in one hour = \frac{1}{8} - \frac{1}{16} = \frac{1}{16} Time required to fill the cistern = 16 hours$

Q16 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 16:

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A pump can fill a tank in 2 hours. Due to a leak in the tank it takes $2 \frac{1}{3}$ hours to fill the tank. The leak can empty the full tank in
(a) $2 \frac{1}{3}$ hours
(b) 7 hours
(c) 8 hours
(d) 14 hours

Answer 16:

(d) 14 hours

$A pump can fill a tank in 2 hours . Part of the tank filled by the pump in one hour = \frac{1}{2} Suppose the leak empties a full tank in x hours . Part of the tank emptied by the leak in one hour = - \frac{1}{x} Part of tank filled in one hour = \frac{1}{2} - \frac{1}{x} = \frac{3}{7} (given) \frac{1}{x} = \frac{1}{2} - \frac{3}{7} = \frac{7 - 6}{14} = \frac{1}{14} x = 14 hours$

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Question 17:

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Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be full?
(a) 7 hrs 15 min
(b) 7 hrs 30 min
(c) 7 hrs 45 min
(d) 8 hrs

Answer 17:

(b) 7 hours 30 minutes

$Part of the tank filled by the first pipe in one hour = \frac{1}{10} Part of the tank filled by the second pipe in one hour = \frac{1}{12} Part of the tank filled by the third pipe in one hour = \frac{- 1}{20} Part of the tank filled by three pipes in one hour = \frac{1}{10} + \frac{1}{12} - \frac{1}{20} = \frac{2}{15} Total time taken to fill the tank = \frac{15}{2} hrs = 7 hours 30 minutes$

RS Aggarwal solution class 8 chapter 13 Time and Work Exercise 13B

Exercise 13B

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Q1 | Ex-13B | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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