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Time And Work - Aptitude MCQ Questions and Solutions with Explanations

Time And Work MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Time And Work with easy and logical explanations. Time And Work MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-9 section-2

Each section contains 100 MCQs on Time and Work .
81
A can complete a piece of work in 10 days, B in 15 days and C in 20 days. A and C together for 2 days and A was replaced by B. In how many days, altogether, was the work complete ?
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & \left( {{\text{A}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{10}} + \frac{1}{{20}}} \right) \cr & = \frac{3}{{20}} \cr & \left( {{\text{A}} + {\text{C}}} \right){\text{'s 2 day's work}} \cr & = \left( {\frac{3}{{20}} \times 2} \right) \cr & = \frac{3}{{10}} \cr & {\text{Remaining work }} \cr & = \left( {1 - \frac{3}{{10}}} \right) \cr & = \frac{7}{{10}}{\text{ }} \cr & \left( {{\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{15}} + \frac{1}{{20}}} \right) \cr & = \frac{7}{{60}} \cr} $$
$$\frac{7}{{60}}$$ work is done by B and C in 1 day
∴ $$\frac{7}{{10}}$$ work is done by B and C in
$$\eqalign{ & = \left( {\frac{{60}}{7} \times \frac{7}{{10}}} \right) \cr & = 6{\text{ days}}{\text{. }} \cr & {\text{Hence, total time taken }} \cr & = \left( {2 + 6} \right){\text{days}} \cr & = 8{\text{ days}} \cr} $$
82
A completes $$\frac{7}{{10}}$$ of the work 15 days. Then he completes the remaining work the help of B in 4 days. The time required for A and B together to complete the entire work is = ?
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 4 day's work}} \cr & = \left( {1 - \frac{7}{{10}}} \right) \cr & = \frac{3}{{10}} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{3}{{10}} \times \frac{1}{4}} \right) \cr & = \frac{3}{{40}} \cr & {\text{Remaining work }} \cr & = \left( {1 - \frac{3}{{10}}} \right) \cr & = \frac{7}{{10}}{\text{ }} \cr & \left( {{\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{15}} + \frac{1}{{20}}} \right) \cr & = \frac{7}{{60}} \cr} $$
Hence, A an B together take $$ = \frac{{40}}{3} = 13\frac{1}{2}$$   days to complete the entire work.
83
A man and a boy can do a piece of work in 24 days. If the man works alone for the last 6 days, it is completed in 26 days. How long would the boy take to do it alone ?
Discuss
Answer & Solution
Answer: Option D
Solution:
(M + B)'s 1 day's work =$$\frac{1}{{24}}$$
(M + B)'s 20 day's work + M's 6 day's work = 1
$$\eqalign{ & \Rightarrow {\text{M's 6 day's work}} \cr & = \left( {1 - \frac{1}{{24}} \times 20} \right) \cr & = \frac{4}{{24}} = \frac{1}{6} \cr & \Rightarrow {\text{M's 1 day's work}} \cr & = \frac{1}{6} \times \frac{1}{6} \cr & = \frac{1}{{36}} \cr & \therefore {\text{B's 1 day's work}} \cr & = \frac{1}{{24}} - \frac{1}{{36}} \cr & = \frac{1}{{72}} \cr} $$
Hence, the boy alone can do the work in 72 days.
84
Two men can do a piece of work in x days. But y women can do that in 3 days. Then the ratio of the work done by 1 man and 1 woman is ?
Discuss
Answer & Solution
Answer: Option A
Solution:
2 men can do a work in x days
1 men can do a work in (2 × x) days
y women can do a work in 3 days
1 women can do a work in 3y days
  1 man   :   1 woman
Days 2x : 3y
Efficiency   3y : 2x

$$\eqalign{ & {\bf{Alternate:}} \cr & {\text{2M}} \times x = y{\text{W}} \times {\text{3}} \cr & \frac{{\text{M}}}{{\text{W}}} = \frac{{3y}}{{2x}} \cr & {\text{M}}:{\text{W}} = 3y:2x \cr} $$
85
If 12 carpenters working 6 hours a day can make 460 chairs in 240 days, then number of chairs made by 18 carpenters in 360 days each working 8 hours a day ?
Discuss
Answer & Solution
Answer: Option B
Solution:
$${\text{According to the question,}}$$
$$ \Rightarrow \frac{{12 \times 6 \times 240}}{{460}}$$     = $$\frac{{18 \times 360 \times 8}}{x}$$
$$\eqalign{ & \Rightarrow x = \frac{{18 \times 360 \times 8 \times 460}}{{12 \times 6 \times 240}} \cr & \Rightarrow x = 1380 \cr} $$
86
A company employed 200 workers to complete a certain work in 150 days. If only $$\frac{1}{4}$$ th of the work had been done in 50 days, then in order to complete the whole work in time, the number of additional workers to be employed were ?
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & \Rightarrow \frac{{{{\text{M}}_1}{{\text{D}}_1}}}{{{{\text{W}}_1}}} = \frac{{{{\text{M}}_2}{{\text{D}}_2}}}{{{{\text{W}}_2}}} \cr & \Rightarrow \frac{{200 \times 50}}{{\frac{1}{4}}} = \frac{{{{\text{M}}_2} \times 100}}{{\frac{3}{4}}} \cr & \Rightarrow {{\text{M}}_2} = 300 \cr & {\text{So, additional men}} \cr & = 300 - 200 \cr & = 100 \cr} $$
87
If 20 women can lay a road of length 100m in 10 days. 10 women can lay the same road of length 50m in = ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{According to the question,}} \cr & \frac{{20 \times 10}}{{100}} = \frac{{10 \times x}}{{50}} \cr & \Leftrightarrow x = 10{\text{ days}} \cr} $$
88
A and B can together finish a work in 30 days. They worked together for 20 days and B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the job ?
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 20 day's work}}{\text{.}} \cr & = \left( {\frac{1}{{30}} \times 20} \right) \cr & = \frac{2}{3} \cr & {\text{Remaining work }} \cr & = \left( {1 - \frac{2}{3}} \right) \cr & = \frac{1}{3}{\text{ }} \cr} $$
Now, $$\frac{1}{3}$$ work is done by A in 20 days
Whole work will be done by A in (20 × 3) = 60 days.
89
A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of the wall ?
Discuss
Answer & Solution
Answer: Option C
Solution:
Part of wall built by A in 1 day = $$\frac{1}{8}$$
Part of wall broken by B in 1 day = $$\frac{1}{3}$$
Part of wall built by A in 4 days
$$\eqalign{ & = \left( {\frac{1}{8} \times 4} \right) \cr & = \frac{1}{2} \cr} $$
Part of wall broken by B and built by A in 2 days
$$\eqalign{ & = 2\left( {\frac{1}{3} - \frac{1}{8}} \right) \cr & = \frac{5}{{12}} \cr} $$
$$\eqalign{ & {\text{Part of wall built in 6 days}} \cr & = \left( {\frac{1}{2} - \frac{5}{{12}}} \right) \cr & = \frac{1}{{12}} \cr & {\text{Remaining part to be built}} \cr & = \left( {1 - \frac{1}{{12}}} \right) \cr & = \frac{{11}}{{12}} \cr} $$
Now, $$\frac{1}{8}$$ part of wall built by A in 1 day
$$\eqalign{ & \therefore \frac{{11}}{{12}}{\text{ part of wall built by A in}} \cr & = \left( {8 \times \frac{{11}}{{12}}} \right) \cr & = \frac{{22}}{3} \cr & = 7\frac{1}{3}{\text{ day}} \cr} $$
90
Anuj and Manoj can together paint their house in 30 days. After working for 20 days, Anuj has to go out and Manoj finished the remaining working the next 30 days. If Manoj had gone away after 20 days instead of Anuj, then Anuj would have completed the remaining work in ?
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & \left( {{\text{Anuj}} + {\text{Manoj}}} \right){\text{'s 20 day's work}} \cr & = \left( {\frac{1}{{30}} \times 20} \right) \cr & = \frac{2}{3} \cr & {\text{Remaining work}} \cr & = \left( {1 - \frac{2}{3}} \right) \cr & = \frac{1}{3} \cr & {\text{Manoj's 30 day's work}} = \frac{1}{3} \cr & \therefore {\text{Manoj's 1 day's work}} = \frac{1}{{90}} \cr & {\text{Anuj's 1 day's work}} \cr & = \left( {\frac{1}{{30}} - \frac{1}{{90}}} \right) \cr & {\text{ = }}\frac{2}{{90}} \cr & = \frac{1}{{45}} \cr} $$
If Manoj had gone away after 20 days, then the remaining $$\frac{1}{3}$$ work would have been done by Anuj.
$$\frac{1}{{45}}$$ work is done by Anuj in 1 day
$$\frac{1}{3}$$ work would be done by Anuj in
$$\eqalign{ & = \left( {45 \times \frac{1}{3}} \right) \cr & = {\text{15 days}} \cr} $$