Time And Work - Aptitude MCQ Questions and Solutions with Explanations

1

A can finish a work in 18 days and B can do the same work in half the time take by A. Then, working together, what part of the same work they can finish in a day ?

A) $$\frac{1}{6}$$ B) $$\frac{1}{9}$$ C) $$\frac{2}{5}$$ D) $$\frac{2}{7}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{A's 1 day's work}} = \frac{1}{{18}} \cr & {\text{And}} \cr & {\text{B's 1 day's work}} = \frac{1}{9} \cr & \therefore \left( {{\text{A}} + {\text{B}}} \right)'{\text{s 1 day's work}} \cr & = \left( {\frac{1}{{18}} + \frac{1}{9}} \right) \cr & = \frac{1}{6} \cr} $$

2

A can knit a pair of socks in 3 days. B can knit the same pair of socks in 9 days. If they are knitting together, then in how many days will they knit two pairs of socks ?

A) 3 days B) 4 days C) $${\text{4}}\frac{1}{2}$$ days D) 5 days

Discuss

Answer & Solution

Answer: Option C

Solution:

Number of pairs knit by A and B together in 1 day
$$\eqalign{ & = \left( {\frac{1}{3} + \frac{1}{9}} \right) \cr & = \frac{4}{9}{\text{ }} \cr} $$
∴ Required number of days,
$$\eqalign{ & = \left( {2 \div \frac{4}{9}} \right) \cr & = \left( {2 \times \frac{9}{4}} \right) \cr & = \frac{9}{2} \cr & = 4\frac{1}{2} \text{ days} \cr} $$

3

P can complete $$\frac{1}{4}$$ of a work in 10 days, Q can complete 40% of the same work in 145 days. R, complete $$\frac{1}{3}$$ of the work in 13 days and S, $$\frac{1}{6}$$ of the work in 7 days. Who will be able complete the work first ?

A) P B) Q C) R D) S

Discuss

Answer & Solution

Answer: Option C

Solution:

P completes $$\frac{1}{4}$$ of work in 10 days
P completes full of work in
$$\eqalign{ & = \frac{{10}}{1} \times 4 \cr & = 40{\text{ days}} \cr} $$
Q completes 40% of work in 145 days
Q completes full 100% of work in
$$\eqalign{ & = \frac{{145}}{{40}} \times 100 \cr & = 362.5{\text{ days}} \cr} $$
R completes $$\frac{1}{3}$$ of work in 13 days
R completes full of work in
$$\eqalign{ & = \frac{{13}}{1} \times 3 \cr & = 39{\text{ days}} \cr} $$
S completes $$\frac{1}{6}$$ of work in 7 days
S completes full of work in
$$\eqalign{ & = \frac{7}{1} \times 6 \cr & = 42{\text{ days}} \cr} $$
Clearly, we can see R completes the work first

4

George takes 8 hours to copy a 50-page manuscript while Sonia can copy the same manuscript in 6 hours. How many hours would it take them to copy a 100-page manuscript, if they work together ?

A) $$6\frac{6}{7}\,\,{\text{hours}}$$ B) $${\text{9 hours}}$$ C) $$9\frac{5}{7}\,\,{\text{hours}}$$ D) $${\text{14 hours}}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

Number of pages typed by Gorge in 1 hour
$$\eqalign{ & = \frac{{50}}{8} \cr & = \frac{{25}}{4} \cr} $$
Number of pages typed by Sonia in 1 hour
$$\eqalign{ & = \frac{{50}}{6} \cr & = \frac{{25}}{3} \cr} $$
Number of pages typed by Gorge and Sonia together in 1 hour
$$\eqalign{ & = \left( {\frac{{25}}{4} + \frac{{25}}{3}} \right) \cr & = \left( {\frac{{75 + 100}}{{12}}} \right) \cr & = \frac{{175}}{{12}} \cr & \therefore {\text{Required time}} \cr & = \left( {100 \div \frac{{175}}{{12}}} \right){\text{hours}} \cr & = \left( {\frac{{100 \times 12}}{{175}}} \right){\text{ hours}} \cr & = \frac{{48}}{7}{\text{ hours}} \cr & = 6\frac{6}{7}{\text{ hours}} \cr} $$

5

A and B together complete a piece of work in T days. If A alone completes the work in T + 3 days and B alone completes the piece of work in T + 12 days, what is T ?

A) 3 days B) 9 days C) 12 days D) Cannot be determined E) None of these

Discuss

Answer & Solution

Answer: Option E

Solution:

$$\eqalign{ & {\text{A's 1 day's work}} \cr & = \frac{1}{{{\text{T}} + 3}} \cr & {\text{B's 1 day's work}} \cr & = \frac{1}{{{\text{T}} + 12}} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} = \frac{1}{{\text{T}}} \cr & \therefore \frac{1}{{{\text{T}} + 3}} + \frac{1}{{{\text{T}} + 12}} = \frac{1}{{\text{T}}} \cr & \Rightarrow \frac{{2{\text{T}} + 15}}{{\left( {{\text{T}} + 3} \right)\left( {{\text{T}} + 12} \right)}} = \frac{1}{{\text{T}}} \cr & \Rightarrow 2{{\text{T}}^2} + 15{\text{T}} = {{\text{T}}^2} + 15{\text{T}} + 36 \cr & \Rightarrow {{\text{T}}^2} = 36 \cr & \Rightarrow {\text{T}} = 6 \cr} $$

6

A can do a piece of work in 20 days and B in 40 days. If they work together for 5 days, then the fraction of the work that is left is ?

A) $$\frac{5}{8}$$ B) $$\frac{8}{{15}}$$ C) $$\frac{7}{{15}}$$ D) $$\frac{1}{{10}}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

L.C.M of total work = 40
One day work of A = $$\frac{{40}}{{20}}$$ = 2 unit/day
One day work of B = $$\frac{{40}}{{40}}$$ = 1 unit/day
(A + B)'s one day work is (2 + 1) units
(A + B)'s 5 day work is 3 × 5 = 15 units
Work left = 40 - 15 = 25
∴ Fraction of work left
$$\eqalign{ & = \frac{{{\text{Work left}}}}{{{\text{Total work}}}} \cr & = \frac{{25}}{{40}} \cr & = \frac{5}{8} \cr} $$

7

If there is a reduction in the number of workers in a factory in the ratio 15 : 11 and an increment in their wages in the rate 22 : 25, then the ratio by which the total wages of the workers should be decreased is = ?

A) 6 : 5 B) 5 : 6 C) 3 : 7 D) 3 : 5

Discuss

Answer & Solution

Answer: Option A

Solution:

	Earlier	:	Now
No.of worker	15	:	11
Wages	22	:	25
Total wages	330		275
Total wages	6	:	5

8

x does $$\frac{1}{4}$$ of a job in 6 days. y completes rest of the job in 12 days. Then x and y could complete the job together in = ?

A) $${\text{9 days}}$$ B) $${\text{8}}\frac{1}{8}{\text{ days}}$$ C) $${\text{9}}\frac{3}{5}{\text{ days}}$$ D) $${\text{7}}\frac{1}{3}{\text{ days}}$$

Discuss

Answer & Solution

Answer: Option C

Solution:

x does $$\frac{1}{4}$$ work in 6 days.
∴ x does complete work in 6 × 4 = 24 days
y does complete the $$\frac{3}{4}$$ work in 12 days.
∴ y does complete work in 12 × $$\frac{4}{3}$$ = 16 days
x and y together can complete a work in
$$\eqalign{ & = \frac{{16 \times 24}}{{16 + 24}} \cr & = \frac{{48}}{5} \cr & = 9\frac{3}{5}\,{\text{days}} \cr} $$

9

Reena, Aastha and Shloka can independently complete a piece of work in 6 hours, 4 hours and 12 hours respectively. If they work together, how much time will they take to complete that piece of work ?

A) 2 hours B) 5 hours C) 6 hours D) 8 hours E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Reena's 1 hour's work}} = \frac{1}{6}{\text{ }} \cr & {\text{Aastha's 1 hour's work}} = \frac{1}{4}{\text{ }} \cr & {\text{Shloka's 1 hour's work}} = \frac{1}{{12}}{\text{ }} \cr} $$

( Reena + Aastha + Shloka )'s 1 hour's work
$$\eqalign{ & = \frac{1}{4} + \frac{1}{6}{\text{ + }}\frac{1}{{12}} \cr & {\text{ = }}\frac{6}{{12}} \cr & = \frac{1}{2} \cr} $$
Hence, Reema, Aastha and Shloka together take 2 hours to complete the work.

10

Amit and Sumit can plough a field in 4 days. Sumit alone can plough the field in 6 days. In how many days will Amit alone plough the feild ?

A) 10 days B) 12 days C) 14 days D) 15 days

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Amit's 1 day's work }} \cr & = \left( {\frac{1}{4} - \frac{1}{6}} \right) \cr & = \frac{1}{{12}} \cr} $$
∴ Amit alone can plough the field in 12 days.