Work and Time Concepts

1. What is Time and work

Time and work is one of the important topics for every competitive exam. Aspirants must know the time and work concepts to score well in quant. section.  Time and work are concerned with the amount of time it takes an individual or a group of individuals to complete a piece of work and the efficiency with which each of them completes it. 

Work: If (T) is the time taken to complete (W) work then the number of units of work done per unit of time is known as the rate of work (R)

Work done(W) = Time (T) x Rate of work(R)

Time: work and time are inversely proportional to each other. Hence, R=

2. Mostly asked questions in Time and Work

The following are the basic types of questions that may be asked in the exam about time and work topic:

• To find the time taken by an individual to complete work.
• To find the time taken by a group of individuals to complete the work.
• To find out the efficiency of the person. 
• Work done by an individual or a group of people in a given time period.

3. Time and work important formula

Important formulas for time and work are given below.

1. Work done= \( \frac{1}{Day} \times Men \times Days \)
2. If A and B can do a piece of work in ‘x’ and ‘y’ days respectively, then their combined rate is: \( \frac{1}{x} + \frac{1}{y} \)
3. Efficiency is inversely proportional to the time taken \( Efficiency=  \frac{1}{Efficiency} \)
4. If three persons (A ,B and C) work together then their combined rate is \( \frac{ABC}{AB+BC+CA} \)
5. If the ratio of time taken by two persons A and B is x:y then the ratio of their efficiency will be y:x

4. Time and work easy tricks

Here are some easy tricks and shortcuts for time and work problems.

• Reciprocal Rule: If A can do a piece of work in x days, A’s work rate is 1/x of the work per day.
• Shortcut of two persons: If A and B work together, their combined rate is \( \frac{A}{A+B} \).
• Shortcut of three people: If A, B and C work together, Their combined rate is \( \frac{A}{A+B+C} \).
• Inverse Relationship: More workers imply less time and vice versa.
• Work efficiency: efficiency and time are reciprocal to each other. If A can complete work in x days then A’s efficiency is 1/x. 
• Alternate Work Approach: If A and B work alternately, their combined rate is \( \frac{1}{A}+\frac{1}{B} \)
• Combine Ratios: If the time ratio of A and B is x:y then the efficiency of A and B is  \( \frac{1}{x}+\frac{1}{y} \).
• Divide and Conquer: Break difficult problems down into simpler components. If multiple workers have different rates, assess each one separately before combining them.

5. Time and work questions and answers

Q1. Ajay can complete a project in 20 days and a simran in 15 days. If they collaborate on it for 5 days, the fraction of the work that remains is 

Ans. Ajay’s 1 day’s work = 1/20

Simran’s 1 day’s work = 1/15

(Ajay+ Simran)’s 1 day’s work = (1/20 + 1/15)  = 7/60

(Ajay+ Simran)’s 5 day’s work = (7/60 × 5) = 7/12

Thus, Remaining work = 1 – 7/12 = 5/12

Q2. Anita can do a piece of work in 25 days whereas Sunita can complete it in 20 days. Both worked together for 5 days and afterward, Anita left the work. How long will B take to complete the remaining work?

Ans. (Anita + Sunita)’s 5 days work = 5(1/25+1/20) = (5*9/100) = 9/20 

Remaining work = (1-9/20) = 11/20 

Sunita finished 1/20 work  in 1 day 

Which means 11/20 work is finished by Sunita in (1*20*11/20) = 11 days

Q3. Lata can do the work in 16 days and Shema can do the work in 12 days. With the help of Praveen, they did the work in 4 days only. Then, Find out How many days can Praveen alone can do the work.

Ans. (Lata + Shema + Praveen)’s 1 day’s work =1/4

Lata’s 1 day’s work = 1/16

Shema’s 1 day’s work = 1/12

Therefore, Praveen’s 1 day’s work 

= 1/4 – (1/16 + 1/12)

= 1/4 – 7/48

= 5/48

Hence, Praveen alone can do the work in 48/5 days.

Q4. A has completed only 1/3rd of the work in 6 days. A took help from B who is 60% as efficient as A. Then how many days more would B take to complete the work?

Ans. 1/3 —- 6

1 ——-? A = 18

R = 1/18 * 60/100 = 1/30

1 —– 1/30

2/3 —-? => 20 days