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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-8 section-3

Each section contains 100 MCQs on Time and Work .
71
A and B can together do a piece of work it in 6 days and A alone can do it in 9 days. The number of days B will take to do it alone is ?
Discuss
Answer & Solution
Answer: Option A
Solution:
L.C.M. of Total Work = 36
One day work of A + B = $$\frac{{36}}{{6}}$$ = 6 unit/day
One day work of A = $$\frac{{36}}{{9}}$$ = 4 unit/day
$$\eqalign{ & {\text{B's efficiency}} \cr & = 6 - 4 \cr & = 2 \cr & {\text{Time taken by B}} \cr & = \frac{{36}}{2} \cr & = 18{\text{ days}} \cr} $$
72
A can do a piece of work in 18 days. He worked at it for 12 days and B finished the remaining work in 8 days. B alone can do the whole work in ?
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{18A}} = {\text{12A}} + {\text{8B}} \cr & {\text{6A}} = {\text{8B}} \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{4}{3} \cr & {\text{So, }} \cr & {\text{Efficiency of A and B are }}4,3. \cr & {\text{Total work}} \cr & = 18 \times 4 \cr & = 72{\text{ units}} \cr & {\text{So, B will do}} \cr & = \frac{{72}}{3} \cr & = 24{\text{ days}} \cr} $$
73
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in ?
Discuss
Answer & Solution
Answer: Option C
Solution:
L.C.M. of Total Work = 24
One day work of A + B = $$\frac{{24}}{{8}}$$ = 3 unit/day
One day work of B + C = $$\frac{{24}}{{12}}$$ = 2 unit/day
One day work of A + B + C = $$\frac{{24}}{{6}}$$ = 4 unit/day
$$\eqalign{ & {\text{Efficiency of C}} \cr & = 4 - 3 \cr & = 1 \cr & {\text{Efficiency of A}} \cr & = 4 - 2 \cr & = 2 \cr & {\text{Efficiency of B}} \cr & = 4 - 1 \cr & = 3 \cr & {\text{Efficiency of A}} + {\text{C}} \cr & = 2 + 1 \cr & = 1 \cr & {\text{Time taken by A}} + {\text{C}} \cr & = \frac{{24}}{3} \cr & = 8{\text{ days}} \cr} $$
74
A can do a certain job in 12 days and B is 60% more efficient than A. The B can do the same piece of work in ?
Discuss
Answer & Solution
Answer: Option B
Solution:
Ratio of time, taken by A and B = 160 : 100 = 8 : 5
If A takes 8 days, B takes 5 days
If A takes 12 days,
B takes $${\text{ = }}\frac{5}{8} \times 12 = \frac{{15}}{2} = 7\frac{1}{2}$$     days
75
A man can do a piece of work in 30 hours. If he works with his son then the same piece of work is finished in 20 hours. If the son works alone then he do the work in ?
Discuss
Answer & Solution
Answer: Option A
Solution:
L.C.M. of Total Work = 60
One hours work of M = $$\frac{{60}}{{30}}$$ = 2 unit/hours
One hours work of M + S = $$\frac{{60}}{{20}}$$ = 3 unit/hours
$$\eqalign{ & {\text{Efficiency of S}} \cr & = 3 - 2 \cr & = 1 \cr & {\text{Required time}} \cr & = \frac{{60}}{1} \cr & {\text{ = }}60{\text{ hours }} \cr} $$
76
The daily wages of A and B respectively are Rs. 3.50 and Rs. 2.50. When A finishes a certain work, he gets a total wage of Rs. 63. When B does the same work, he gets a total wage Rs. 75. If both of them do it together what is cost of the work ?
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{Worked day of A}} \cr & = \frac{{63}}{{3.50}} = 18{\text{ days}} \cr & {\text{Worked day of B}} \cr & = \frac{{75}}{{2.50}} = 30{\text{ days}} \cr & {\text{Now, }} \cr} $$
L.C.M. of Total Work =90
One day work of A = $$\frac{{90}}{{18}}$$ = 5 unit/day
One day work of B = $$\frac{{90}}{{30}}$$ = 3 unit/day
$$\eqalign{ & {\text{Required time}} \cr & = \frac{{90}}{8} = \frac{{45}}{4}{\text{ days}} \cr & {\text{Cost}} = {\text{day}} \times \left( {{\text{wages of A}} + {\text{B}}} \right) \cr & = \frac{{45}}{4} \times \left( {3.50 + 2.50} \right) \cr & = {\text{Rs}}.\,67.50 \cr} $$
77
A man does double the work done by a boy in the same time. The number of days that 3 men and 4 boys will take to finish a work which can be done by 10 men in 8 days is ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & \frac{{\text{M}}}{{\text{B}}} = \frac{2}{1}\left( {{\text{Efficiency}}} \right) \cr & {\text{Now,given}} \cr & \left( {{\text{3M}} + {\text{4B}}} \right) \times {\text{D}} = 10 \times 2 \times 8 \cr & \left( {{\text{3}} \times 2 + 4 \times 1} \right) \times {\text{D}} = 10 \times 2 \times 8 \cr & 10 \times {\text{D}} = 10 \times 16 \cr & {\text{D}} = 16{\text{ days}} \cr} $$
78
P can do $$\frac{1}{4}$$ th of work in 10 days. Q can do 40% of work in 40 days and R can do $$\frac{1}{3}$$ rd of work in 13 days. Who will complete the work first ?
Discuss
Answer & Solution
Answer: Option C
Solution:
P complete $$\frac{1}{4}$$ th of work in 10 days
So, P will complete the whole work in 40 days.
Q completes $$\left( {40\% = \frac{2}{5}{\text{th}}} \right)$$   work in 40 days
Q will complete the whole work in = $$\frac{{40 \times 5}}{2}$$ = 100 days
R completes $$\frac{1}{3}$$ work in 13 days
R will complete the whole work in = 39 days
Work will be finished firstly by the man who will take less days to complete it,
So, R will complete it first.
79
The time taken by 4 men to complete a job is double the time taken by 5 children to complete the same job. Each man is twice as fast as a woman. How long will 12 men, 10 children and 8 women take to complete a job, given that a child would finish the job in 20 days ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{By using formula}} \cr & {{\text{M}}_1}{{\text{D}}_1}{{\text{H}}_1} = {{\text{M}}_2}{{\text{D}}_2}{{\text{H}}_2} \cr & {\text{According to the question,}} \cr & {\text{5C}} = {\text{4M}} \times {\text{2}} \cr & \frac{{\text{M}}}{{\text{C}}} = \frac{5}{8}\left( {{\text{Efficiency ratio}}} \right) \cr & {\text{Again,}} \cr & \frac{{\text{M}}}{{\text{W}}} = \frac{2}{1}\left( {{\text{Efficiency ratio}}} \right) \cr & \,\,\,\,{\text{M }}:{\text{ W }}:{\text{ C}} \cr & \,\,\,\,{{\text{2}}_{ \times 5}}:{\text{ }}{1_{ \times 5}} \cr & \,\,\,\,{5_{ \times 2}}:\,\,\,\,\,\,\,\,\,\,\,\,\,\,{8_2} \cr & \overline {{\text{ }}10{\text{ }}:{\text{ }}5{\text{ }}:{\text{ }}16{\text{ }}} \cr & {\text{Now, }} \cr & {\text{20C}} = \left( {{\text{12M}} + {\text{10C}} + {\text{8W}}} \right) \times {\text{D}} \cr} $$
$$20 \times 16 = $$   $$\left( {12 \times 10 + 10 \times 16 + 8 \times 5} \right)$$     $$ \times {\text{D}}$$
$$\eqalign{ & 320 = 320{\text{D}} \cr & {\text{D}} = \frac{{320}}{{320}} = 1 \cr & \boxed{{\text{D}} = 1{\text{ day}}} \cr} $$
80
The labourers A, B, C were given a contract of Rs. 750 for doing a certain piece of work. All the three together can finish the work in 8 days, A and C together can do it 12 days, while A and B together can do it in $${\text{13}}\frac{1}{3}$$ days. The money will be divided in the ratio ?
Discuss
Answer & Solution
Answer: Option A
Solution:
L.C.M. of Total Work = 120
One day work of A + B + C = $$\frac{{120}}{{8}}$$ = 15 unit/day
One day work of A + B = $$\frac{{120}}{{\frac{{40}}{3}}}$$ = 9 unit/day
One day work of A + C = $$\frac{{120}}{{12}}$$ = 10 unit/day
$$\eqalign{ & {\text{C's efficiency}} = 15 - 9 = 6 \cr & {\text{B's efficiency}} = 15 - 10 = 5 \cr & {\text{A's efficiency}} = 15 - \left( {6 + 5} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15 - 11 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4 \cr & {\text{So, A}}:{\text{B}}:{\text{C}} = 4:5:6 \cr} $$