Time and Work MCQ Quiz - Objective Question with Answer for Time and Work - Download Free PDF
Last updated on Jun 16, 2025
Latest Time and Work MCQ Objective Questions
Time and Work Question 1:
X, Y, and Z together can finish a piece of work in [P/13] days, while X and Y together can do it in [P/10] days. Y alone can complete the same work in [P/4] days. Z takes 20 days more than X to complete the work alone. What is the value of P?
Answer (Detailed Solution Below)
Time and Work Question 1 Detailed Solution
Calculation
One day work of X, Y & Z together = 13/P
One day work of X & Y together = 10/ P
One day work of Z = 13 / P – 10/ P = 3 /P
Time taken by Z alone to complete the work = P/3 days
One day work of X & Y together = 10/P
One day work Y = 4 / P
One day work X = 10 /P - 4 /P = 6 /P
Time taken by X alone to complete the work = P / 6 days
ATQ, P/ 3 − P /6 = 20
Or, P/ 6 = 20
So, P = 120
Time and Work Question 2:
A alone can do a work in 18 days, while A and B together can do the same work in 12 days. Find in how many days B alone can do the same work?
Answer (Detailed Solution Below)
Time and Work Question 2 Detailed Solution
Given:
A can do the work in 18 days
A and B together can do the work in 12 days
Formula used:
Work = LCM of days taken
Efficiency = Work ÷ Time
Time taken by B = Total work ÷ (Efficiency of B)
Calculations:
LCM of 18 and 12 = 36 (since HCF = 6)
⇒ Total work = 36 units
⇒ A’s 1 day work = 36 ÷ 18 = 2 units
⇒ A and B’s 1 day work = 36 ÷ 12 = 3 units
⇒ B’s 1 day work = 3 - 2 = 1 unit
⇒ Time taken by B = 36 ÷ 1 = 36 days
∴ B alone can do the work in 36 days.
Time and Work Question 3:
X, Y, and Z together can finish a piece of work in [P/13] days, while X and Y together can do it in [P/10] days. Y alone can complete the same work in [P/4] days. Z takes 20 days more than X to complete the work alone. What is the value of P?
Answer (Detailed Solution Below)
Time and Work Question 3 Detailed Solution
Calculation
One day work of X, Y & Z together = 13/P
One day work of X & Y together = 10/ P
One day work of Z = 13 / P – 10/ P = 3 /P
Time taken by Z alone to complete the work = P/3 days
One day work of X & Y together = 10/P
One day work Y = 4 / P
One day work X = 10 /P - 4 /P = 6 /P
Time taken by X alone to complete the work = P / 6 days
ATQ, P/ 3 − P /6 = 20
Or, P/ 6 = 20
So, P = 120
Time and Work Question 4:
A group of 5 men or 12 women can complete a particular task in 78 days. How long will it take for 5 men and 12 women working together to finish the same task?
Answer (Detailed Solution Below)
Time and Work Question 4 Detailed Solution
Given:
5 men can complete a task in 78 days.
12 women can complete the same task in 78 days.
Formula used:
If M1 persons can do a work in D1 days, and M2 persons can do the same work in D2 days, then M1D1 = M2D2.
Also, Work = Efficiency × Time
Calculations:
5 men ≡ 12 women
5 men and 12 women:
Total equivalent men = 5 men (from the group of men) + 5 men (equivalent to 12 women)
⇒ Total equivalent men = 10 men
We know that 5 men can complete the task in 78 days.
Let D be the number of days 10 men will take.
Using the formula M1D1 = M2D2:
5 × 78 = 10 × D
⇒ D = (5 × 78) / 10
⇒ D = 78 / 2
⇒ D = 39 days
∴ It will take 39 days for 5 men and 12 women working together to finish the same task.
Time and Work Question 5:
If 2 men and 4 boys can finish a job in 8 days and 3 men and 2 boys can finish it in 6 days, how many days will 12 boys take to finish the same ?
Answer (Detailed Solution Below)
Time and Work Question 5 Detailed Solution
Given:
2 men and 4 boys can finish a job in 8 days.
3 men and 2 boys can finish the job in 6 days.
Formula used:
Let the work done by 1 man in 1 day = M units, and the work done by 1 boy in 1 day = B units.
Work = Total units of work
Calculations:
From the first equation, the total work done by 2 men and 4 boys in 1 day is:
(2M + 4B) × 8 = Total work (W)
⇒ 2M + 4B = W/8 (Equation 1)
From the second equation, the total work done by 3 men and 2 boys in 1 day is:
(3M + 2B) × 6 = Total work (W)
⇒ 3M + 2B = W/6 (Equation 2)
Now solve these two equations simultaneously:
From Equation 1: 2M + 4B = W/8
From Equation 2: 3M + 2B = W/6
Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate variables:
6M + 12B = 3W/8 (Equation 3)
6M + 4B = W/3 (Equation 4)
Now subtract Equation 4 from Equation 3:
(6M + 12B) - (6M + 4B) = (3W/8) - (W/3)
⇒ 8B = (9W - 8W) / 24
⇒ 8B = W/24
⇒ B = W/192
Now substitute B = W/192 into Equation 1:
2M + 4(W/192) = W/8
⇒ 2M + W/48 = W/8
⇒ 2M = W/8 - W/48 = 5W/48
⇒ M = 5W/96
Now, we need to find how many days 12 boys will take to complete the work. The work done by 12 boys in one day is:
12B = 12 × (W/192) = W/16
The total time taken by 12 boys is:
Time = Total work / Work done by 12 boys in 1 day = W / (W/16) = 16 days
∴ 12 boys will take 16 days to finish the job.
Top Time and Work MCQ Objective Questions
A cistern has two pipes one can fill it with water in 16 hours and other can empty it in 10 hours. In how many hours will the cistern be emptied if both the pipes are opened together when 1/5th of the cistern is already filled with water?
Answer (Detailed Solution Below)
Time and Work Question 6 Detailed Solution
Download Solution PDFShortcut Trick
If both pipes are open, total efficiency = (A + B) = 5 + (-8) = -3 units
According to question,
Amount of water in the tank = (1/5) × 80 = 16 units
Time taken to empty the tank = work/efficiency = 16/((-3)) = 5.33 hours
Alternate Method
GIVEN :
Time by which pipe A can fill the tank = 16 hours
Time by which pipe B can empty the tank = 10 hours
The cistern is (1/5)th full.
CONCEPT :
Total work = time × efficiency
CALCULATION :
| Work | Time | Efficiency |
| A | 16 | 80/16 = 5 |
| B | 10 | 80/10 = (-8) |
|
total work (LCM) |
80 |
Negative efficiency indicates pipe B is emptying the tank.
If both pipes are open, total efficiency = (A + B) = 5 + (-8) = -3 units
From the total efficiency it is clear that when both are opened, the tank is being emptied.
Amount of water in the tank = (1/5) × 80 = 16 units
The water level will not rise as the total action is emptying when both are opened together.
Time taken to empty the tank = work/efficiency = 16/((-3)) = 5.33 hours
∴ Time taken to empty the tank is 5.33 hours.
Harish and Bimal can complete a task in 20 days. They worked at it for 15 days and then Bimal left. The remaining work was done by Harish alone, in 10 days. Harish alone can complete the entire task in:
Answer (Detailed Solution Below)
Time and Work Question 7 Detailed Solution
Download Solution PDFGiven:
No of days taken by Harish and Bimal = 20
Formula used:
No of days taken = Work/Efficiency
Calculation:
Let the total work be = 1
One day work done by Harish and Bimal = 1/20
Work done by Harish and Bimal in 15 days = 1/20 × 15 = 3/4
⇒ Remaining work = 1 - 3/4 = 1/4
Harish did remaining work in 10 days alone.
⇒ One day work done by Harish = 1/4 ÷ 10 = 1/40
∴ Time taken by Harish to do the entire task alone = 1 ÷ 1/40 = 40 days
Shortcut TrickFraction of work done by Harish & Bimal in 15 days = 15/20 = 3/4
The remaining 1/4th (25%) of work was done by Harish in 10 days.
∴ The 100% work would be done by Harish in (10 × 4) 40 days.
A and B together can do a piece of work in 50 days. If A is 40% less efficient than B, in how many days can A working alone complete 60% of the work?
Answer (Detailed Solution Below)
Time and Work Question 8 Detailed Solution
Download Solution PDFGiven:
A and B together can do a piece of work in 50 days.
A is 40% less efficient than B
Concept used:
Total work = Efficiency of the workers × time taken by them
Calculation:
Let the efficiency of B be 5a
So, efficiency of A = 5a × 60%
⇒ 3a
So, total efficiency of them = 8a
Total work = 8a × 50
⇒ 400a
Now,
60% of the work = 400a × 60%
⇒ 240a
Now,
Required time = 240a/3a
⇒ 80 days
∴ A can complete 60% of the work working alone in 80 days.
Shortcut Trick
We know 40% = 2/5, Efficiency of B = 5 and A = 3
So, Total work = (5 + 3) × 50 = 400 units
So, 60% of the total work = 60% of 400 = 240 units
So A alone can do the work in 240/3 = 80 days
A can finish a work in 15 days, B can finish the same work in 25 days. They work together for 5 days. The rest of the work is finished by A and C in 4 days. Then C alone can finish the work in:
Answer (Detailed Solution Below)
Time and Work Question 9 Detailed Solution
Download Solution PDFGiven:
A can finish in 15 days, B can finish it in 25 days.
They work together for 5 days.
Concept used:
Efficiency = (Total work / Total time taken)
Efficiency = work done in a single day
Calculation:
Let total work be 75 units ( LCM of 15 and 25 is 75)
The efficiency of A
⇒ 75 /15 = 5 units
The efficiency of B
⇒ 75 / 25 = 3 units
The efficiency of A+B,
⇒ (5 + 3) units = 8 units
In 5 days total work done is 8 × 5 = 40 units
Remaining work 75 - 40 = 35 units
In the last 4 days, A does 4 × 5 = 20 units
Remaining work 35 - 20 = 15 units done by C in 4 days
So C does 75 units in (75 / 15) × 4 = 20 days
∴ The correct option is 3
A and B together are supposed to do 13/15 of the work and B and C together 11/20 of the work. If the difference between wages of A and C is Rs. 7600, then the total wages of A and C is:
Answer (Detailed Solution Below)
Time and Work Question 10 Detailed Solution
Download Solution PDFGiven:
Difference between wages of A and C = Rs. 7600
Formula Used:
Share in wages = Work done/Total work × Total wages
Calculation:
Let total work be 60 unit,
Work done by A and B = 13/15 × 60 = 52 unit
⇒ Work done by C = 60 – 52 = 8 unit
Work done by B and C = 11/20 × 60 = 33 unit
⇒ Work done by A = 60 – 33 = 27 unit
Work done by B = 60 – 27 – 8 = 25 unit
According to the question,
27 – 8 = 19 unit = 7600
⇒ 1 unit = 400
Total wages of A and C = (27 + 8) = 35 units = 35 × 400 = Rs. 14000
23 people could do a piece of work in 18 days. After 6 days 8 of the workers left. How many days from then will it take to complete the work?
Answer (Detailed Solution Below)
Time and Work Question 11 Detailed Solution
Download Solution PDFGiven:
23 people could do a piece of work in 18 days.
After 6 days 8 of the workers left.
Concept used:
Total work = Men needed × Days needed to finish it entirely
Calculation:
Total work = 23 × 18 = 414 units
In 6 days, total work done = 23 × 6 = 138 units
Remaining work = (414 - 138) = 276 units
Time taken to complete the remaining work = 276 ÷ (23 - 8) = 18.4 days
∴ 18.4 days it will take to finish the work.
The efficiency of A, B, and C is 2 : 3 : 5. A alone can complete a work in 50 days. They all work together for 5 days and then C left the work, in how many days A and B together can complete the remaining work?
Answer (Detailed Solution Below)
Time and Work Question 12 Detailed Solution
Download Solution PDFGiven:
Efficiency of A, B and C = 2 : 3 : 5
A alone can complete the work in = 50 days
Formula:
Total work = Efficiency × Time
Calculation:
Let efficiency of A be 2 units/day
Efficiency of A, B and C = 2 : 3 : 5
Total work = 2 × 50 = 100 units
Work done by A, B and C in 5 days = (2 + 3 + 5) × 5 = 10 × 5 = 50 units
Remaining work = 100 – 50 = 50 units
∴ Time taken by A and B to complete the remaining work = 50/(2 + 3) = 50/5 = 10 days
Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?
Answer (Detailed Solution Below)
Time and Work Question 13 Detailed Solution
Download Solution PDFGiven:
First pipe can fill the cistern = 3 hours
Second pipe can fill the cistern = 4 hours
Third pipe can drain the cistern = 8 hours
Calculation:
Let the total amount of work in filling a cistern be 24 units. (LCM of 3, 4 and 8)
Work done by pipe 1 in 1 hour = 24/3 = 8 units.
Work done by pipe 2 in 1 hour = 24/4 = 6 units.
Work done by pipe 3 in 1 hour = 24/ (-8) = -3 units
Total work done in 1 hour = 8 + 6 – 3 = 11 units
The time required to complete 11/12th of the work = 11/12 × 24/ 11 = 2 hours
∴ The correct answer is 2 hours.
A,B and C can do a piece of work in 30 days, 40 days and 50 days, respectively. Beginning with A, if A, B and C do the work alternatively then in how many days will the work be finished?
Answer (Detailed Solution Below)
Time and Work Question 14 Detailed Solution
Download Solution PDFGiven:
A can do a piece of work = 30 days
B can do a piece of work = 40 days
C can do a piece of work = 50 days
Formula used:
Total work = efficiency × time
Calculation:
| Efficiency | Person | Time | Total work |
| 20 | A | 30 | 600 |
| 15 | B | 40 | |
| 12 | C | 50 |
According to the question:
⇒ (20 + 15 + 12) = 47 units = 3 days
⇒ 47 × 12 = 564 units = 3 × 12 = 36 days
⇒ (564 + 20 + 15) = 599 units = 38 days
Total work = 600 units = 38 + (1/12) = 38
∴ The correct answer is 38
If 'A' is 6 times more efficient than 'B', 'B' takes 32 days to complete the task, then find the number of days required to finish the whole work by 'A' and 'B' working together.
Answer (Detailed Solution Below)
Time and Work Question 15 Detailed Solution
Download Solution PDFGiven:
A is 6 times more efficient than B, & B takes 32 days to complete the task.
Formula used:
Total work = Efficiency × Time taken
Calculation:
A is 6 times more efficient than B
Efficiency of A ∶ Efficiency of B = 7 ∶ 1
Total work = Efficiency of B × Time taken
⇒ 1 × 32 = 32 units
Number of days required to finish the whole work by (A + B) = Total work/Efficiency of (A+ B)
⇒ 32/8
⇒ 4
∴ The total number of days required to finish the whole work by (A + B) is 4 days.
There is a difference in "Efficient" and " More efficient"
A is 6 times efficient than B means if B is 1 then, A will be 6
A is 6 times more efficient than B means if B is 1 then, A will be (1 + 6) = 7
In the question, it is given that A is 6 times more efficient which means if B is 1, then A will (1 + 6) times = 7 times efficient
So, Total efficiency of A and B = (1 + 7) = 8 units/day
Time taken to complete the work together = 32/8 days
⇒ 4 days and this is the answer.