Time and Work

Quantitative Aptitude Questions and Answers section on “Time and Work” with solution and explanation for competitive examinations such as CAT, MBA, SSC, Bank PO, Bank Clerical and other examinations.
1.

A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?
[A]5.4 days
[B]7.5 days
[C]3.6 days
[D]3 days

3.6 days
According to question. A can finish the whole work in 6 days.
∴ A’s one day’s work =\frac{1}{6}
Similiarly, B’s one day’s work =\frac{1}{9}
(A+B)’s one day’s work = \left ( \frac{1}{6}+\frac{1}{9} \right )=\left ( \frac{3+2}{18} \right )=\frac{5}{18}
Therefore, (A+B) can finish the whole work in \frac{18}{5} days i.e. 3.6 days.
Hence option [C] is the right answer.

2.

A and B together can complete a work in 8 days and B and C together in 12 days. All of the three together can complete the work in 6days. In how much time will A and C together complete the work?
[A]20
[B]8
[C]12
[D]10

8
Let A and C complete the work in x days
(A+B)’s one day’s work= \frac{1}{8}
(B+C)’s one day’s work= \frac{1}{12}
(C+A)’s one day’s work= \frac{1}{x}
Then (A+B+B+C+C+A)’s one day’s work = \frac{1}{8}+\frac{1}{12}+\frac{1}{x}
2(A+B+C)’s one day’s work = \frac{3x+2x+24}{24x}
(A+B+C)’s 1 day’s work = \frac{5x+24}{24x\times 2}
According to the question (A+B+C)’s 1 day’s work = \frac{1}{6}
=>\frac{1}{6} = \frac{5x+24}{24x\times 2}
=> 30x + 144 = 48x
∴ x = \frac{144}{18} = 8 days
∴ option [B] is the right answer.

3.

A and B together can do a piece of work in 10 days. A alone can do it in 30 days. The time in which B alone can do it is :
[A]10
[B]12
[C]20
[D]15

15
(A+B)’s 1 day’s work = \frac{1}{10}
A’s 1 day’s work = \frac{1}{30}
∴ B’s 1 day’s work = \frac{1}{10}-\frac{1}{30}
=\frac{3-1}{30}=\frac{2}{30}=\frac{1}{15}
Hence, B, alone can complete the work in 15 days.

4.

A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they wil complete the same work in :
[A]4 days
[B]\frac{1}{4} days
[C]3\frac{3}{7} days
[D]\frac{7}{24} days

\mathbf{3\frac{3}{7}} days
A’s 1 day’s work = \frac{1}{24}
B’s 1 day’s work = \frac{1}{6}
C’s 1 day’s work = \frac{1}{12}
(A+B+C)’s 1 day’s work = \frac{1}{24}+\frac{1}{6}+\frac{1}{12}=\frac{1+4+2}{24}=\frac{7}{24}
∴ The work will be completed by them in \frac{24}{7} i.e. 3\frac{3}{7} days.

5.

A and B together can complete a piece of work in 72 days, B and C together can complete it in 120 days, and A and C together in 90 days. In what time can A alone complete the work?
[A]150 days
[B]80 days
[C]100 days
[D]120 dyas

120 days
(A+B)’s 1 day’s work = \frac{1}{72}
(B+C)’s 1 day’s work = \frac{1}{120}
(C+A)’s 1 day’s work = \frac{1}{90}
Adding all three, 2(A+B+C)’s 1 days work = \frac{1}{72}+\frac{1}{120}+\frac{1}{90}
=> \frac{5+3+4}{360}=\frac{12}{360}=\frac{1}{30}
∴ (A+B+C)’s 1 day’s work = \frac{1}{60}
Now, A’s 1 day’s work = (A+B+C)’s 1 day’s work – (B+C)’s 1 day’s work
=>\frac{1}{60}-\frac{1}{120}=\frac{2-1}{120}=\frac{1}{120}
∴ A alone can comlete the work in 120 days.
Hence option [D] is correct.

6.

A alone can complete a work in 12 days. A and B together can complete it in 8 days. How long will B alone take to complete the work?
[A]20 days
[B]24 days
[C]16 days
[D]18 days

24 days
A’s one day’s work = \frac{1}{12}
(A + B)’s one day’s work = \frac{1}{8}
∴ B’s one day’s work =
= \frac{1}{8} - \frac{1}{12} = \frac{3-2}{24} = \frac{1}{24}
∴ B alone can do the work in 24 days.
Hence option [B] is the right answer.

7.

A can do a piece of work in 4 hours, B and C can do it in 3 hours. A and C can do it in 2 hours. How long will B alone take to do it?
[A]8 hours
[B]24 hours
[C]10 hours
[D]12 hours

12 hours
A’s one hour’s work = \frac{1}{4}
(B + C)’s one hour’s work = \frac{1}{3}
(A + C)’s one hour’s work = \frac{1}{2}
∴ C’s one hour’s work = \frac{1}{2}-\frac{1}{4} = \frac{2-1}{4} = \frac{1}{4}
B’s one hour’s work = \frac{1}{3}-\frac{1}{4} = \frac{4-3}{12} = \frac{1}{12}
Hence B alone can do the work in 12 hours, so option [D] is correct answer.

8.

A and B can do a work in 12 days, B and C in 15 days and C and A in 20 days. If A, B and C work together, they will complete the work in :
[A]15\frac{2}{3} days
[B]5 days
[C]10 days
[D]7\frac{5}{6} days

10 days
According to question,
A and B can do a work in 12 days
∴ (A + B)’s one day’s work = \frac{1}{12}
Similarly, (B + C)’s one day’s work = \frac{1}{15}
and (C + A)’s one day’s work = \frac{1}{20}
On adding all three,
∴ 2 (A + B + C)’s one day’s work = \frac{1}{12}+ \frac{1}{15}+ \frac{1}{20}
= \frac{10+8+6}{120} = \frac{1}{5}
and (A + B + C)’s one day’s work = \frac{1}{10}
∴ A, B and C together can complete the work in 10 days.

9.

A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C can do it in 90 days. In how many days all the three together can do the work ?
[A]150 days
[B]60 days
[C]80 days
[D]100 days

60 days
According to question,
(A + B)’s one day’s work = \frac{1}{72}
(B + C)’s one day’s work = \frac{1}{120}
and (C + A)’s one day’s work = \frac{1}{90}
On adding all three,
2 (A + B + C)’s one day’s work = \frac{1}{72}+ \frac{1}{120}+ \frac{1}{90}
= \frac{5+3+4}{360} = \frac{1}{30}
∴ (A + B + C)’s one day’s work = \frac{1}{60}
∴ A, B and C together can finish the whole work in 60 days.
Hence option [B] is the right answer.

10.

A paricular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to complete the job if the two teams work together?
[A]18 days
[B]9 days
[C]6 days
[D]4 days

4 days
According to the question,
10 men’s one day’s work = \frac{1}{12}
∴ 1 man one day’s work = \frac{1}{12\times 10} = \frac{1}{120}
Similarly,
1 woman one day’s work = \frac{1}{6\times 10} = \frac{1}{60}
∴ (1 man + 1 woman)’s one day’s work =  \frac{1}{120}+\frac{1}{60}
= \frac{1+2}{120} = \frac{3}{120} = \frac{1}{40}
∴ (10 man + 10 woman)’s one day’s work =  \frac{10}{40} = \frac{1}{4}
Therefore, both the team can finish the whole work in 4 days.
Hence option [D] is the right answer.



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