Time And Work - Aptitude MCQ Questions and Solutions with Explanations

Answer: Option A

1^st method:
A and B complete a work in = 15 days
One day's work of (A + B) = $$\frac{1}{{15}}$$
B complete the work in = 20 days;
One day's work of B = $$\frac{1}{{20}}$$
Then, A's one day's work
$$\eqalign{ & = \frac{1}{{15}} - \frac{1}{{20}} \cr & = \frac{{4 - 3}}{6} \cr & = \frac{1}{{60}} \cr} $$
Thus, A can complete the work in = 60 days.

2^nd method:
(A + B)'s one day's % work = $$\frac{{100}}{{15}}$$ = 6.66%
B's one day's % work = $$\frac{{100}}{{20}}$$ = 5%
A's one day's % work = 6.66 - 5 = 1.66%
Thus, A need = $$\frac{{100}}{{1.66}}$$ = 60 days to complete the work.

Answer: Option B

$$\eqalign{ & {\text{One}}\,{\text{day's}}\,{\text{work}}\,{\text{of}} \cr & \left( {A + B} \right) = \frac{1}{{18}}\,.......(1) \cr & {\text{One}}\,{\text{day's}}\,{\text{work}}\,{\text{of}} \cr & \left( {A + C} \right) = \frac{1}{{12}}\,.......\left( 2 \right) \cr & {\text{One}}\,{\text{day's}}\,{\text{work}}\,{\text{of}} \cr & \left( {B + C} \right) = \frac{1}{9}\,.......\left( 3 \right) \cr & {\text{Adding}}\,\left( {\text{1}} \right){\text{,}}\,\left( {\text{2}} \right)\,{\text{and}}\,\left( {\text{3}} \right) \cr & 2 \times \left( {A + B + C} \right) = { {\frac{1}{{18}}} + {\frac{1}{{12}}} + {\frac{1}{9}} } \cr & 2(A + B + C) = \frac{1}{4} \cr & {\text{One day's work of}} \cr & {A + B + C} = \frac{1}{8} \cr & B = {\frac{1}{8}} - \left( {A + C} \right) \cr & B = {\frac{1}{8}} - {\frac{1}{{12}}} \cr & {\text{One day's work of}} \cr & B = \frac{{ {3 - 2} }}{{24}} = \frac{1}{{24}} \cr & B\,{\text{need}}\,24\,{\text{days}} \cr} $$

Answer: Option B

1^st Method:
(A+B)'s one day's work = $$\frac{1}{3}$$ part
(A+B) works 2 days together = $$\frac{2}{3}$$ part
Remaining work = $$1 - \frac{2}{3}$$  = $$\frac{1}{3}$$ part
$$\frac{1}{3}$$ part of work is completed by A in two days
Hence, one day's work of A = $$\frac{1}{6}$$
Then, one day's work of B = $$\frac{1}{3} - \frac{1}{6}$$  = $$\frac{1}{6}$$
So, B alone can complete the whole work in 6 days.

2^nd Method:
(A+B)'s one day's % work = $$\frac{{100}}{3}$$ = 33.3%
Work completed in 2 days = 66.6%
Remaining work = 33.4%
One day's % work of A = $$\frac{{33.4}}{2}$$ = 16.7%
One day's work of B = 33.4 - 16.7 = 16.7%
B alone can complete the work in,
= $$\frac{{100}}{{16.7}}$$
= 5.98 days
≈ 6 days.

Answer: Option C

1^st Method:
$$\eqalign{ & \left( {B + C} \right)\,2\,{\text{days}}\,{\text{work}} \cr & = 2 \times \left( {\frac{1}{{20}} + \frac{1}{{30}}} \right) \cr & = 2 \times {\frac{{3 + 2}}{{60}}} \cr & = \frac{1}{6}{\text{part}} \cr & {\text{Remaining}}\,{\text{work}} \cr & = 1 - \frac{1}{6} \cr & = \frac{5}{6}\text{part} \cr & {\text{A's}}\,{\text{one}}\,{\text{day's}}\,{\text{work}} \cr & = \frac{1}{{18}}{\text{part}} \cr & {\text{Time taken to complete the work}} \cr & = \frac{{ {\frac{5}{6}} }}{{ {\frac{1}{{18}}} }}\,{\text{days}} \cr & {\text{Hence,}} \cr & {\text{Time taken to complete the work}} \cr & = {\frac{5}{6}} \times 18 \cr & = 15\,{\text{days}} \cr} $$

2^nd Method:
% of work B completes in one day = $$\frac{{100}}{{20}}$$ = 5%;
% of work C completes in one day = $$\frac{{100}}{{30}}$$ = 3.33%;
% of work (A + B) completes together in one day = 5 + 3.33 = 8.33%;
% work (A + B) completes together in 2 days = 8.66 × 2 = 16.66%;
Remaining work = 100 - 16.66 = 83.34%;
% of work A completes in 1 day = $$\frac{{100}}{{18}}$$ = 5.55%
Time taken to complete the remaining work by A
= $$\frac{{83.34}}{{5.55}}$$
= 15 days

Answer: Option A

1^st Method:
Working 5 hours a day, A can complete the work in 8 days i.e.
= 5 × 8 = 40 hours
Working 6 hours a day, B can complete the work in 10 days i.e.
= 6 × 10 = 60 hours
(A + B)'s 1 hour's work,
$$\eqalign{ & = \frac{1}{{40}} + \frac{1}{{60}} \cr & = \frac{{3 + 2}}{{120}} \cr & = \frac{5}{{120}} \cr & = \frac{1}{{24}} \cr} $$
Hence, A and B can complete the work in 24 hours i.e. they require 3 days to complete the work.

2^nd Method:
% 1 hour's work of A = $$\frac{{100}}{{40}}$$ = 2.5%
% 1 hour's work of B = $$\frac{{100}}{{60}}$$ = 1.66%
(A + B) one hour's % work,
= (2.5 + 1.66) = 4.16%
Time to complete the work,
= $$\frac{{100}}{{4.16}}$$ = 24 hours
Then, $$\frac{{24}}{8}$$ = 3 days
They need 3 days, working 8 hours a day to complete the work.