Time And Work - Aptitude MCQ Questions and Solutions with Explanations

41

A is 40% more efficient than B and C is 20% less efficient than B. Working together, they can finish a task in 15 days. In how many days, will B alone complete 75% of the task?

A) 36 B) 48 C) 32 D) 44

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & \left( {7 + 5 + 4} \right) \times 15 \times \frac{{75}}{{100}} = {\text{B}} \times 5 \cr & {\text{B}} = 36{\text{ days}} \cr} $$

42

A takes twice as much time as B and thrice as much time as C to finalise a task. Working together, they can complete the task in 8 days. The time (in days) taken by A, B and C, respectively, to complete the task is:

A) 42, 21, 14 B) 60, 30, 20 C) 54, 27, 18 D) 48, 24, 16

Discuss

Answer & Solution

Answer: Option D

Solution:

Efficiency of A : B : C = 1 : 2 : 3
Total work = 8 × (A + B + C) = 48
Time taken by A → $$\frac{{48}}{1}$$ = 48 days
Time taken by B → $$\frac{{48}}{2}$$ = 24 days
Time taken by C → $$\frac{{48}}{3}$$ = 16 days

43

Raju can finish a piece of work in 20 days. He worked at it for 5 days and then Jakob alone finished the remaining work in 15 days. In how many days can both finish it together?

A) 10 days B) 12 days C) 16 days D) 20 days

Discuss

Answer & Solution

Answer: Option A

Solution:

Let total work = 60 unit
Work by Raju in one day = $$\frac{{60}}{{20}}$$ = 3 unit
5 days → 5 × 3 = 15 unit
Remaining work = 60 - 15 = 45 unit
15 days → 45 unit
1 day → 3 unit (Jakob)
Work done by Raja and Jakob in one day = 3 + 3 = 6
Time = $$\frac{{60}}{6}$$ = 10 days

44

A and B undertake a contract of a task for Rs. 10,800. A and B can complete the task in 45 days and 60 days, respectively. However, to finish the work early, they take C's help and complete the entire work in 20 days. What is the value (in Rs.) of (a - b + 2c), where a, b and c are the shares of A, B and C, respectively, for their contribution to complete the task?

A) 3000 B) 6000 C) 4000 D) 8000

Discuss

Answer & Solution

Answer: Option B

Solution:

Efficiency,
A ⟶ 4 = a
B ⟶ 3 = b
C ⟶ 2 = c
9μ ⟶ 10800
1μ ⟶ 1200
a - b + 2c
= 4 - 3 + 4
= 5μ
= 5 × 1200
= 6000 Answer

45

A alone can do a work in 11 days. B alone can do the same work in 22 days. C alone can do the same work in 33 days. They work in the following manner:
Day 1: A and B work.
Day 2: B and C work.
Day 3: C and A work.
Day 4: A and B work. And so on.
In how many days will the work be completed?

A) 3 days B) 12 days C) 6 days D) 9 days

Discuss

Answer & Solution

Answer: Option D

Solution:

First day work done (A + B) = 6 + 3 = 9
Second day work done (B + C) = 3 + 2 = 5
Third day work done (C + A) = 2 + 6 = 8
Time and Work mcq question image

46

The ratio of the efficiencies of A, B and C is 7 : 5 : 8. Working together, they can complete a piece of work in 42 days. B and C worked together for 21 days and the remaining work was completed by A alone. The whole work was completed in:

A) 96 days B) 99 days C) 102 days D) 93 days

Discuss

Answer & Solution

Answer: Option C

Solution:

A : B : C = 7 : 5 : 8
20 × 42 = 21(B + C) + A × D days
20 × 42 = 21 × 13 × 7 × D
120 = 39 + D
D = 81
21 days, worked already
Total = 21 + 81 = 102 days

47

X can do a work in 3 days, Y does three times the same work in 8 days, and Z does five times the same work in 12 days. If they have to work together for 6 hours in a day, then in how much time can they complete the work?

A) 4 hours B) 5 hours 20 minutes C) 4 hours 10 minutes D) 5 hours

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{So, required answer}} \cr & = \left( {\frac{{24}}{{8 + 9 + 10}}} \right) \times 6{\text{ hr/day}} \cr & = \frac{{48}}{9} \cr & = \frac{{16}}{3} \cr & = 5{\text{ hr }}20\,\min \cr} $$

48

P can work thrice as fast as Q working independently, can complete a task in 24 days. In how many days can P and Q together finish the same task?

A) 5 B) 4 C) 6 D) 8

Discuss

Answer & Solution

Answer: Option C

Solution:

\[\begin{array}{*{20}{c}} {}&{\text{P}}&{}&{\text{Q}} \\ {{\text{Efficiency}}}&3&:&1 \\ {{\text{Time}}}&1&:&3 \end{array}\]
3 unit → 24 days
1 unit → 8 days
Total work = 24
P + Q can complete the same work = $$\frac{{24}}{4}$$ = 6 days

49

A alone can do a work in 14 days. B alone can do the same work in 28 days. C alone can do the same work in 56 days. They start the work together and completed the work such that B was not working on last 2 days and A did not work in last 3 days. In how many days (total) was the work completed?

A) $$\frac{{72}}{7}$$ B) $$\frac{{79}}{7}$$ C) $$\frac{{65}}{7}$$ D) $$\frac{{82}}{7}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

Work done not done by B = 2 × 2 = 4
Work done not done by A = 3 × 4 = 12
Total work = 56 + 4 + 12 = 72
∴ Total time $$ = \frac{{72}}{{4 + 2 + 1}} = \frac{{72}}{7}{\text{days}}$$

50

A and B can do a work together in 18 days. A is three time as efficient as B. In how many days can B alone complete the work?

A) 60 days B) 72 days C) 54 days D) 64 days

Discuss

Answer & Solution

Answer: Option B

Solution:

A : B = 3 : 1
Total work = 4 × 18 = 72 unit
B = \[\frac{{72}}{1}\] = 72 days