Time and Work | Quantitative Aptitude

 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

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.

What is Time and Work?

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.

Types of Questions from Time and Work

There are some specific types of questions from Time and Work that usually come in exams. Some of the important types of questions from time and work are as follows:

Time and Work Questions involving individual efficiencies

In such questions, the rates at which some individuals complete work alone are given and you are required to calculate the rate at which they can complete the work together and vice versa.

Time and Work Questions involving group efficiencies 

Till now, we have looked at problem types where individuals were working, in this type of question, we will now look at problems where people with the same efficiencies are working in groups.

Tips and Tricks to Solve Questions based on Time and Work

Candidates can find different tips and tricks from below for solving the questions related to time and work.

Tip # 1: Work and Wages Concept: Ratio of wages of persons doing work is directly proportional to the ratio of efficiency of the persons.

Tip # 2: If A can do a piece of work in 10 days, then in 1 day, A will do 1/10 part of total work.

Tip # 3:If A is thrice as good as B, then

1. In a given amount of time, A will be able to do 3 times the work B does. Ratio of work done by A and B (at the same time) = 3 : 1.
2. For the same amount of work, B will take thrice the time as much as A takes. Ratio of time taken by A and B (same work done) = 1 : 3.

Tip # 4: Efficiency is directly proportional to the work done and Inversely Proportional to the time taken.

Tip # 5: The number of days or time required to complete the work by A and B both is equal to the ab/a+b.

Solved Questions on Time and Work

Example 1: A alone can do a job in 40 days. In how many days can B alone do the job, if together they can do the job in 8 days?

Solution: ⇒ Efficiency of A: Efficiency of A + B = (1/40) ∶ (1/8) = 1 ∶ 5

⇒ Efficiency of B / Efficiency of A = (5 – 1)/1 = 4/1 B is 4 times efficient than A,

⇒ Number of days taken by B = 1/4 × Number of days taken by A = 40/4 = 10 days

Example 2: A does work in 10 days and B does the same work in 15 days. In how many days they together will do the same work?

Solution: A + B = 3 + 2 unit/day = 5 units/day

Time = 30 / 5 = 6 days.

Example 3: A and B can do a work in 3 days; B & C can do it in 4 days and A & C can do it in 6 days. In how many days will A, B & C finish it, if they work together?

Solution: A + B + C = 9/2

Time = 12 / (9/2) = 8/3 days

Example 4: A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How long would A take separately to do the same work?

Solution: One day work of A and B = 1/12 One day work of B and C = 1/15 One day work of C and A = 1/20

One day work of (A + B), (B + C) and (C + A) = 1/12 + 1/15 + 1/20

= 12/60 = 1/5

One day work of (A + B + C) = (1/2) × (1/5) = 1/10

One day work of A = One day work of (A + B + C) – One day work of (B + C)

= 1/10 – 1/15 = 2/60 = 1/30

∴ A takes 30 days alone to do the same work.

Example 5: P is twice as good as Q and together they finish a piece of work in 36 days. The number of days taken by P alone to finish the work?

Solution: Given,

P is twice as good as Q.

⇒ (P’s 1 day’s work) / (Q’s 1 day’s work) = 2 / 1 Given,

⇒ (P + Q)’s 1 day’s work = 1/36

⇒ P’s 1 day’s work = (1/36) × (2/3) = 1/54

∴ P alone can finish work in 54 days.

Example 6: P, Q and R can complete work for Rs. 21000. P, Q and R can alone complete work in 20 days, 30 days and 60 days respectively. With help of D they complete work in 8 days. Among the four who gets the highest share and how much?

Solution: Given,

⇒ P’s 1 day’s work = 1/20

⇒ Q’s 1 day’s work = 1/30

⇒ R’s 1 day’s work = 1/60

(P + Q + R)’s 1 days work = 1/20 + 1/30 + 1/60 = (6/60) = 1/10 (P + Q + R + D)’s 1 days work = 1/8

D’s 1 day’s work = 1/8 – 1/10 = 2/80 = 1/40

Ratio of work efficiency = P : Q : R : D = 1/20 : 1/30 : 1/60 : 1/40 = 6 : 4 : 2 : 3

⇒ P’ share = 21000 × 6/15 = Rs. 8400

⇒ Q’ share = 21000 × 4/15 = Rs. 5600

⇒ R’ share = 21000 × 2/15 = Rs. 2800

⇒ S’ share = 21000 × 3/15 = Rs. 4200

∴ From this, P gets the highest share of Rs. 8400.

Example 7: A and B can complete a piece of work in 15 days and 10 days respectively.

They got a contract to complete the work for Rs. 75000. The share of B (in Rs.) in the contracted money will be:

Solution: Ratio of number of days taken by A and B to complete the work = 15 : 10 = 3 : 2

∴ Ratio of efficiency of A and B = 2 : 3 Let their share is in the ratio of 2x and 3x Now,

2x + 3x = 75000

⇒ 5x = 75000

∴ x = 15000

∴ Share of B = 3x = 15000 × 3 = RS. 45000

Example 8: 30 men are engaged to a work by a contractor for 6 days. They work for 4 days but due to some reasons, only 50% of the work will be completed. How many more men should be engaged to work to complete the work in a given period of time.

Solution: Given time = 6 days Total men = 30

let the extra men be x So, 30 × 4 = (30 + x) 2

So, x = 30 men

Example 9: A town with a population of 4000 had food packets for 30 days. After 10 days 1000 more people are added. How long will the food packets last now?

Solution: Town with a population of 4000 had food packets for 30 days.

∴ Total food packets = 4000 × 30 = 120000 Other 1000 people joined after 10 days.

Food packet consumed in first 10 days = 4000 × 10 = 40000.

∴ Remaining food packets = 120000 – 40000 = 80000 Now 1000 people more are added

∴ Total people = 4000 + 1000 = 5000.

Now, remaining food packets will be divided among 5000 people.

∴ No. of days food will last = Remaining food packets/No. of people

⇒ No. of days food will last = 80000/5000

⇒ No. of days food will last = 16

We hope you found this article regarding Time and Work informative and helpful, and please do not hesitate to contact us for any doubts or queries regarding the same. You can also download the Itselfu RBI Grade'B'App, which is absolutely free and start preparing for any government competitive examination by taking the mock tests before the examination to boost your preparation.