Time and Work Questions PDF for SSC, Railways and Banking Exams
Time and Work Questions PDF for SSC, Railways and Banking Exams

Quant Booster Dose –  Time and Work Questions PDF

Time and Work Question PDF with Answers for government exams like SSC, Railways, Banking, FCI, CWC, Insurance Exams, UPSC, and other state PCS exams. As we all know in many competitive exams in Quantitative Aptitude/ Numerical Ability subject Time and Work Questions asked repeatedly, so you cannot ignore the Time and Work Questions PDF.

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Time and Work Questions PDF for SSC, Railways and Banking Exams

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Time and Work Questions with Answers | Download Free PDF

What is Time and Work?

Time and work are concerned with the time taken by a person or a group of persons to complete a task and the efficiency of the work done by each of them. Time and work problems are important because there is a certain relationship between the number of persons doing the work, number of days or time taken by them to complete the work and the amount of work that is done.

Work done = Number of persons x Number of days

W = M x D

Time: Time is the duration during which any activity or work happens or continues.

Work: Work is a task or set of activities to achieve a certain result.

Here the unit of work is man days or man hours. The problems of time and work can primarily be divided into two types. This type includes problems where individuals work with different efficiencies either alone or in combination to complete a task. The second type includes problems where group efficiencies are involved.

The important terms related to time and work are given below:

Time Taken: Rate of work and time are inversely proportional to each other. Thus, R = 1/T

Work Done: It takes (T) time to complete a certain amount of work (W). The number of units of work done per unit time. Thus, Work Done (W) = Time (T) * Rate of Work (R)

Negative Work: Assume that there are two people A and B who have been assigned to build a table. Here, work refers to the building of a table. Also, assume that there is another person C who is assigned the task of damaging the table. Now, work done by C is termed as negative work as C is effectively lowering the amount of work done by A and B.

Work Equivalence: Please note that the work one by people/pipes can be stated mathematically as,

Work done = rate of work x time

Consider the following formula also,

M1D1T1 = M2D2T2 (provided work remains the same)

In the above formula,

M = Number of persons

D = Number of days

T = Number of hours.

The equation is called the “work equivalence formula”

Concept of Efficiency: Very often, you will get to read and solve time-work problems where it is usually mentioned that the efficiency of A is twice the efficiency of B or that A is three times more efficient than B. In the first case, it means that A takes one-half of the time taken by B to do the same amount of work. In the second case, it means that A’s efficiency is thrice that of B and so A will take one-third of the time taken by B to do the same amount of work.

Important Time and Work Formula

Given below are a few such important time and work formulas for your reference:

  • Work Done = Time Taken × Rate of Work
  • Rate of Work = 1 / Time Taken
  • Time Taken = 1 / Rate of Work
  • If a piece of work is done in x number of days, then the work done in one day = 1/x
  • Total Wok Done = Number of Days × Efficiency
  • Efficiency and Time are inversely proportional to each other
  • X:y is the ratio of the number of men which are required to complete a piece of work, then the ratio of the time taken by them to complete the work will be y:x
  • If x number of people can do W1 work, in D1 days, working T1 hours each day and the number of people can do W2 work, in D2 days, working T2 hours each day, then the relation between them will be

uploaded image

Time and Work Shortcut – Fraction Conversion? 

Number of days required to complete the work Work that can be done per day Efficiency in Percent
n 1/n (100/n)%
1 1/1 100%
2 1/2 50%
3 1/3 33.33%
4 1/4 25%
5 1/5 20%
6 1/6 16.66%
7 1/7 14.28%
8 1/8 12.5%
9 1/9 11.11%
10 1/10 10%
11 1/11 9.09%

Time and Work Practice Questions with Answers

1. Four taps can individually fill a cistern of water in 1 hour, 2 hours, 3 hours and 6 hours respectively. If all the four taps are opened simultaneously, the cistern can be filled in how many minutes ?

(a) 20

(b) 30

(c) 35

(d) 40

(e) None of these

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Correct Answer:  (b) 30

Explanation:  References

1662464224414image7

2 . ‘X’ completes a job in 2 days and ‘Y’ completes it in 3 days and ‘Z’ takes 4 days to complete it. If they work together and get Rs. 3,900 for the job, then how much amount does ‘Y’ get ?

(a) Rs. 1,800

(b) Rs. 1,200

(c) Rs. 900

(d) Rs. 800

(e) None of these

Show Correct Answers

Correct Answer:  (b) Rs. 1,200

Explanation:  References

1662464224414image8

3. In order to fill an empty pond with water, two pipes A and B are engaged. Pipe A alone can fill the pond in 70 hours and pipe B alone can fill it in 80 hours. If both the pipes A and B are opened simultaneously, how much time will be required to fill the pond?

(a) 27.30 hours

(b) 25.85 hours

(c) 37.33 hours

(d) 32.45 hours

(e) None of these

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Correct Answer:  (c) 37.33 hours

Explanation:  Pipe A fills the pond in 70 hours.

Pipe B fills the pond in 80 hours.

Calculations:

Rate of Pipe A = 1/70 ponds per hour

Rate of Pipe B = 1/80 ponds per hour

Combined rate of A and B:

⇒ Rate = (1/70 + 1/80) ponds per hour

Finding a common denominator:

⇒ Common denominator = 560

⇒ Rate = (8/560 + 7/560) = 15/560 ponds per hour

To find the time taken to fill the pond, we use:

Time = 1 pond / (15/560) ponds per hour

⇒ Time = 560 / 15 hours

⇒ Time = 37.33 hours

4. 40 workers can complete a 100 m long road-repairing job in 50 days. In order to complete the same task in 40 days, how many additional workers are required?

(a) 12

(b) 15

(c) 18

(d) 10

(e) None of these

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Correct Answer:  (d) 10

Explanation:  40 workers can complete a 100 m long road-repairing job in 50 days.

We need to complete the same task in 40 days.

Formula Used:

Work = Number of Workers × Number of Days

Calculation:

Initial Work = 40 workers × 50 days

Initial Work = 2000 worker-days

Required Work = Number of Workers × 40 days

To complete the same work in 40 days:

2000 worker-days = Number of Workers × 40 days

⇒ Number of Workers = 2000 worker-days / 40 days

⇒ Number of Workers = 50

Additional Workers Required = 50 – 40

Additional Workers Required = 10

= Rs. 4760

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5. B1, B2 and B3 can do a work in 10, 5 and 7.5 days respectively. All three of them began the work together but B2 left 1.5 days before the completion of the work. In how many days was the work completed?

(a) 6 days

(b) 4 days

(c) 3 days

(d) 5 days

(e) None of these

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Correct Answer:  (c) 3 days

Explanation:  B1 can do the work in 10 days.

B2 can do the work in 5 days.

B3 can do the work in 7.5 days.

B2 left 1.5 days before the completion of the work.

Formula Used:

Total Work = Work done by B1 + Work done by B2 + Work done by B3

Calculation:

Total units of work = LCM of 10, 5, 7.5 = 30 units

Efficiency of B1 = 30/10 = 3

Efficiency of B2 = 30/5 = 6

Efficiency of B3 = 30/7.5 = 4

Let the total number of days to complete the work be x.

Then, in (x – 1.5) days, B2 worked together with B1 and B3, and for the remaining 1.5 days, only B1 and B3 worked.

Work done by B1 + Work done by B2 + Work done by B3 = Total Work

⇒ (x – 1.5) × 6 + x(3 + 4) = 30

⇒ 13x = 39

⇒ x = 39/13

⇒ x = 3

6. The time taken by Pipe A to fill the tank is 3 hours more than that of Pipe B. Pipe A and B together can fill the tank in 20/3 hours. Find the time taken by Pipe A alone to fill the whole tank.

(a) 16 hours

(b) 15 hours

(c) 12 hours

(d) 18 hours

(e) None of these

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Correct Answer:  (b) 15 hours

Explanation:  Pipe B alone fill the whole tank = x

Pipe A alone fill the whole tank = x + 3

1/(x + 3) + 1/x = 1/(20/3)

1/(x + 3) + 1/x = 3/20

x + x + 3 = 3/20 (x² + 3x)

20 (2x + 3) = 3 (x² + 3x)

40x + 60 = 3x² + 9x

3x² – 31x – 60 = 0

3x² – 36x + 5x – 60 = 0

3x (x – 12) + 5 (x – 12) = 0

(3x + 5) (x – 12) = 0

x = – 5/3, x = 12

Negative value won’t come because both the pipes can fill the tank

So, x = 12

So, A alone can fill the whole tank = 15 hours

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7. 18 men can complete the work in 20 days. 15 women can complete the same work in 12 days. In how many days, 6 men and 4 women can complete the same piece of work?

(a) 140/3 days

(b) 150/7 days

(c) 180/7 days

(d) 160/7 days

(e) None of these

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Correct Answer:  (c) 180/7 days

Explanation:  Efficiency of men = m

Efficiency of women = w

18 x m x 20 = 15 x w x 12

2 x m = 1 x w

m/w = 1/2

Total work = 18 x 1 x 20 = 360

Required days = 360/(6 x 1 + 4 x 2)

= 360/(6 + 8)

= 360/14

= 180/7 days

8. 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?

(a) 70

(b) 110

(c) 80

(d) 105

(e) None of these

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Correct Answer:  (c) 80

Explanation:  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.

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9. 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:

(a) 18 days

(b) 24 days

(c) 20 days

(d) 21 days

(e) None of these

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Correct Answer:  (c) 20 days

Explanation:  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

10. 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?

(a) 17.6

(b) 18.4

(c) 20.4

(d) 16.8

(e) None of these

Show Correct Answers

Correct Answer:  (b) 18.4

Explanation:  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

All the Time and Work questions are formulated as per the level of Bank PO exams. The Time and Work questions in this PDF has a moderate and hard level of difficulty. All the candidates who are preparing for banking exams are advised to practice all these important questions to score well in the exam. To remove any doubt or difficulty in any topic, go through the study notes of each topic from the links given above.

Why Quantitative Aptitude Time and Work Questions PDF is Important for Exams?

  • All the questions prepare by Exams experts.
  • The practice questions covered are across the levels i.e. Easy, Moderate, and Difficult.
  • Provides a detailed approach to the solution of each question.
  • Focuses on all the new patterns and advanced-level type questions.
  • Time and Work Questions PDF boosts confidence and reduces pre-exam jitters by regularly attempting a variety of questions and tackling the difficulty level expected in the final exam.

This Quant Booster Dose Time and Work Questions PDF is useful for the upcoming Banking and Insurance exams i.e. IBPS PO, SBI PO, Clerk, IBPS RRB PO & Clerk, RBI Assistant, RBI Grade B, NABARD, LIC AAO, SSC (CGL, CHSL, MTS, CPO, and Constable), Railway RRB (NTPC, Group D, JE, ALP) & Other Government Exams.

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8700+ Quantitative Aptitude Topic wise Questions and Answers – Download Free PDF

8700+ Quantitative Aptitude Topic wise Questions and Answers – Download Free PDF

Quant Booster Dose – Topic-wise Quantitative Aptitude Questions and Answers