Time and work: Class 8 practice
If A finishes a job in a days, A does 1/a of it each day. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Adding fractions
- Reciprocals
The idea behind time and work
If A finishes a job in a days, A does 1/a of it each day. Working together, the daily fractions add: time = 1 ÷ (1/a + 1/b).
Step-by-step method
- Write each person's work per day.
- Add the fractions for working together.
- Time = 1 ÷ (combined work per day).
Worked example 1 (Basic)
A can finish a job in 6 days and B in 3 days. How long together?
- Per day: 1/6 + 1/3 = 1/2
- Time = 2 days
- Answer: 2 days
Worked example 2 (Standard)
A can finish a job in 10 days and B in 15 days. How long together?
- Per day: 1/10 + 1/15 = 1/6
- Time = 6 days
- Answer: 6 days
Worked example 3 (Challenge)
A and B together finish a job in 4 days. A alone takes 12 days. How long does B take alone?
- 1/B = 1/4 − 1/12
- B = 6 days
- Answer: 6 days
Common mistakes and misconceptions
- Adding the days instead of the rates
- Forgetting to take the reciprocal at the end
Practice questions
- (Basic) A can finish a job in 12 days and B in 6 days. How long together?
- (Basic) A can finish a job in 8 days and B in 24 days. How long together?
- (Standard) A can finish a job in 20 days and B in 30 days. How long together?
- (Standard) A can finish a job in 18 days and B in 9 days. How long together?
- (Challenge) A and B together finish a job in 2 days. A alone takes 6 days. How long does B take alone?
- (Challenge) A and B together finish a job in 3 days. A alone takes 12 days. How long does B take alone?
Answer key with full working
- Q1: Per day: 1/12 + 1/6 = 1/4 → Time = 4 days → Answer: 4 days
- Q2: Per day: 1/8 + 1/24 = 1/6 → Time = 6 days → Answer: 6 days
- Q3: Per day: 1/20 + 1/30 = 1/12 → Time = 12 days → Answer: 12 days
- Q4: Per day: 1/18 + 1/9 = 1/6 → Time = 6 days → Answer: 6 days
- Q5: 1/B = 1/2 − 1/6 → B = 3 days → Answer: 3 days
- Q6: 1/B = 1/3 − 1/12 → B = 4 days → Answer: 4 days
Syllabus note
This skill is listed under "Direct and Inverse Proportions" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is time and work in?
"Direct and Inverse Proportions", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.