Inverse proportion problems: Class 8 practice
Two quantities are inversely proportional when one increases as the other decreases so that their product stays constant: x₁y₁ = x₂y₂.. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Unitary method
The idea behind inverse proportion problems
Two quantities are inversely proportional when one increases as the other decreases so that their product stays constant: x₁y₁ = x₂y₂.
Step-by-step method
- Decide whether the relation is direct or inverse.
- For inverse: x₁ × y₁ = x₂ × y₂.
- Solve for the unknown.
Worked example 1 (Basic)
5 workers take 72 days to finish a job. How long will 6 workers take?
- Product stays the same: 5 × 72 = 360
- 360 ÷ 6 = 60
- Answer: 60 days
Worked example 2 (Standard)
6 taps take 30 minutes to fill a tank. How long will 2 taps take?
- Product stays the same: 6 × 30 = 180
- 180 ÷ 2 = 90
- Answer: 90 minutes
Worked example 3 (Challenge)
10 pipes take 18 hours to fill a tank. How long will 4 pipes take?
- Product stays the same: 10 × 18 = 180
- 180 ÷ 4 = 45
- Answer: 45 hours
Common mistakes and misconceptions
- Treating it as direct proportion
- Not checking whether the answer makes sense
Practice questions
- (Basic) 12 workers take 15 days to finish a job. How long will 3 workers take?
- (Basic) 24 workers take 6 days to finish a job. How long will 9 workers take?
- (Standard) 18 taps take 10 minutes to fill a tank. How long will 3 taps take?
- (Standard) 6 taps take 60 minutes to fill a tank. How long will 30 taps take?
- (Challenge) 2 pipes take 72 hours to fill a tank. How long will 9 pipes take?
- (Challenge) 12 pipes take 20 hours to fill a tank. How long will 30 pipes take?
Answer key with full working
- Q1: Product stays the same: 12 × 15 = 180 → 180 ÷ 3 = 60 → Answer: 60 days
- Q2: Product stays the same: 24 × 6 = 144 → 144 ÷ 9 = 16 → Answer: 16 days
- Q3: Product stays the same: 18 × 10 = 180 → 180 ÷ 3 = 60 → Answer: 60 minutes
- Q4: Product stays the same: 6 × 60 = 360 → 360 ÷ 30 = 12 → Answer: 12 minutes
- Q5: Product stays the same: 2 × 72 = 144 → 144 ÷ 9 = 16 → Answer: 16 hours
- Q6: Product stays the same: 12 × 20 = 240 → 240 ÷ 30 = 8 → Answer: 8 hours
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 inverse proportion problems 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.