Class 8 - Time and work

Time and Work is a concept that deals with how long it takes for one person or a group of people to complete a task, and how efficient they are in doing it. These problems study the relationship between three things the number of people working, the time they take, and the total work completed.

What is Time and Work?

Time and Work is a basic concept in mathematics that explains how long a person or a group takes to complete a task. Time and Work shows the connection between work, time, and speed of working.

Time and Work Definition

Time and Work is defined as: The relationship between the total work, the time taken to complete it, and the rate at which the work is done.

Time and Work Formula

• 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

M1×D1×T1W1=M2×D2×T2W2

Time and Work Solved Problems

Problem 1: A can complete a work in 12 days. How much work does he complete in 1 day?

Solution:

Step 1: Total work = 1

Step 2: Time = 12 days

Step 3: Work done in 1 day = 1 ÷ 12

Answer: A completes 1/12 of the work in one day.

Problem 2: A can finish a work in 10 days and B can finish the same work in 5 days. How long will they take if they work together?

Solution:

Step 1: A’s one day work = 1/10

B’s one day work = 1/5

Step 2: Total work in one day = 1/10 + 1/5

Convert to same denominator: 1/10 + 2/10 = 3/10

Step 3: Time = 1 ÷ (3/10) = 10/3 days

Answer: They will complete the work in 10/3 days (3⅓ days).

Problem 3: A can complete a work in 15 days. B can complete it in 20 days. How much work do they complete together in 1 day?

Solution:

Step 1: A’s one day work = 1/15

B’s one day work = 1/20

Step 2: Total work in one day = 1/15 + 1/20

LCM = 60

= 4/60 + 3/60 = 7/60

Answer: Together they complete 7/60 of the work in one day

Problem 4: A can complete a work in 8 days. He works for 2 days and then leaves. How much work is left?

Solution:

Step 1: A’s one day work = 1/8

Step 2: Work done in 2 days = 2 × (1/8) = 2/8 = 1/4

Step 3: Remaining work = 1 − 1/4 = 3/4

Answer: 3/4 of the work is left

Problem 5: A and B together can complete a work in 6 days. If A alone can complete it in 10 days, how long will B take alone?

Solution:

Step 1: (A + B)’s one day work = 1/6

A’s one day work = 1/10

Step 2: B’s one day work = 1/6 − 1/10

LCM = 30

= 5/30 − 3/30

= 2/30

= 1/15

Step 3: Time taken by B = 15 days

Answer: B alone will complete the work in 15 days