# TIME AND WORK RELATED QUESTIONS AND ANSWERS ## Time and Work

Time and Work is one of the most common quantitative aptitude topics which is asked in the Government exams. This is one of those topics which candidates are familiar with even before they start their competitive exam preparation. The concept of time and work remains the same, however, the type of questions asked may have a bit of variety. Mostly, 1-2 words problems are asked from this topic but candidates must also keep themselves prepared to have questions in data sufficiency and data interpretation to be picked up from time and work.

## Introduction and Concept

Before we move on to the questions and important formulas, it is important that a candidate is well aware of the concept and the types of questions which may be asked in the exam. Time and work deals with the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the work done by each of them.

Given below are the basic type of questions which may be asked in the exam with respect to the time and work topic:

• To find the efficiency of a person
• To find the time taken by an individual to do a piece of work
• To find the time taken by a group of individuals to complete a piece of work
• Work done by an individual in a certain time duration
• Work done by a group of individuals in a certain time duration

Mostly the questions asked may involve one of these things to find and candidates can use the related formulas to easily get through the answers for the same.

## Important Time and Work Formula

Knowing the formulas can completely link you to a solution as soon as you read the question. Thus, knowing the formula for any numerical ability topic make the solution and the related calculations simpler.

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

Aspirants for the various Government exams must start their preparation now to ensure they give their 100 per cent and complete hard work and dedication to their preparation.

Questions:

1.

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

A.

 1 4

B.

 1 10

C.

 7 15

D.

 8 15

Explanation:

 A's 1 day's work = 1 ; 15

 B's 1 day's work = 1 ; 20

 (A + B)'s 1 day's work = 1 + 1 = 7 . 15 20 60

 (A + B)'s 4 day's work = 7 x 4 = 7 . 60 15

 Therefore, Remaining work = 1 - 7 = 8 . 15 15

2.

A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:

A.

 9 1 days 5

B.

 9 2 days 5

C.

 9 3 days 5

D.

10

Explanation:

 (A + B + C)'s 1 day's work = 1 , 4

 A's 1 day's work = 1 , 16

 B's 1 day's work = 1 . 12

 C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 5 . 4 16 12 4 48 48

 So, C alone can do the work in 48 = 9 3 days. 5 5

3.

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

 A. 12 days B. 15 days C. 16 days D. 18 days

Explanation:

 A's 2 day's work = 1 x 2 = 1 . 20 10

 (A + B + C)'s 1 day's work = 1 + 1 + 1 = 6 = 1 . 20 30 60 60 10

 Work done in 3 days = 1 + 1 = 1 . 10 10 5

 Now, 1 work is done in 3 days. 5

Whole work will be done in (3 x 5) = 15 days.

4.

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

A.

20 days

B.

 22 1 days 2

C.

25 days

D.

30 days

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

 If difference of time is 60 days, B takes 3 x 60 = 90 days. 2

So, A takes 30 days to do the work.

 A's 1 day's work = 1 30

 B's 1 day's work = 1 90

 (A + B)'s 1 day's work = 1 + 1 = 4 = 2 30 90 90 45

 A and B together can do the work in 45 = 22 1 days. 2 2

5.

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

 A. Rs. 375 B. Rs. 400 C. Rs. 600 D. Rs. 800

Explanation:

 C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 1 . 3 6 8 3 24 24

 A's wages : B's wages : C's wages = 1 : 1 : 1 = 4 : 3 : 1. 6 8 24

 C's share (for 3 days) = Rs. 3 x 1 x 3200 = Rs. 400. 24

1. Dev completed the school project in 20 days. How many days will Arun take to complete the same work if he is 25% more efficient than Dev?
2. 10 days
3. 12 days
4. 16 days
5. 15 days
6. 5 days

Answer: (c) 16 days

Solution:

Let the days taken by Arun to complete the work be x

The ratio of time taken by Arun and Dev = 125:100 = 5:4

5:4 :: 20:x

⇒ x = {(4×20) / 5}

⇒ x = 16

1. Time taken by A to finish a piece of work is twice the time taken B and thrice the time taken by C. If all three of them work together, it takes them 2 days to complete the entire work. How much work was done by B alone?
2. 2 days
3. 6 days
4. 3 days
5. 5 days
6. Cannot be determined

Answer: (2) 6 days

Solution:

Time taken by A  = x days

Time taken by B = x/2 days

Time Taken by C = x/3 days

⇒ {(1/x) + (2/x) + (3/x) = 1/2

⇒ 6/x = 1/2

⇒ x = 12

Time taken by B = x/2 = 12/2 = 6 days

1. Sonal and Preeti started working on a project and they can complete the project in 30 days. Sonal worked for 16 days and Preeti completed the remaining work in 44 days. How many days would Preeti have taken to complete the entire project all by herself?
2. 20 days
3. 25 days
4. 55 days
5. 46 days
6. 60 days

Answer: (5) 60 days

Solution:

Let the work done by Sonal in 1 day be x

Let the work done by Preeti in 1 day be y

Then, x+y = 1/30 ——— (1)

⇒ 16x + 44y = 1  ——— (2)

Solving equation (1) and (2),

x = 1/60

y = 1/60

Thus, Preeti can complete the entire work in 60 days

1. A can do a bit of work in 10 days while B alone can do it in 15 days. They cooperate for 5 days and whatever remains of the work is finished by C in 2 days. On the off chance that they get Rs. 4500 for the entire work, by what means if they partition the cash?
2. Rs 1250, Rs 1200, Rs 550
3. Rs 2250, Rs 1500, Rs 750
4. Rs 1050, Rs 1000, Rs 500
5. Rs 650, Rs 700, Rs 500

Explanation

(A+B)'s 5 days work = 5(1/10+ 1/15)= (5* 1/6)= 5/6

Remaining work = (1-5/6) = 1/6

C's 2 days work = 1/6

(A's 5 day work): (B's 5 day work): (C's 2 days work)

= 5/10: 5/15: 1/6

= 15: 10:5 = 3:2:1

A's offer = (4500*3/6) = Rs. 2250

B's offer = (4500*2/6) = Rs. 1500

C's share= (4500*1/6) = Rs. 750

1. Ajay and Vijay undertake to do a piece of work for Rs. 480. Ajay alone can do it in 75 days while Vijay alone can do it in 40 days. With the help of Pradeep, they finish the work in 25 days. How much should Pradeep get for his work?
2. 40
3. 20
4. 360
5. 100
6. 60

Sol : Option 2
Explanation:In 24 days, they would have done 1/3 and 5/8 of the work.
The remaining work is 1 – (1/3 + 5/8) = 1/24.
This means Pradeep has done 1/24th of the work, so he should be paid 1/24th of the amount i.e. 480 × 1/24 = Rs. 20 is the answer.