Extra Questions for Class 8 Maths Chapter 10: Proportional Reasoning 2 – HOTS

Original HOTS-level (Higher Order Thinking Skills) practice questions for Class 8 Maths Chapter 10 (Proportional Reasoning 2), genuinely harder than the textbook exercise, using fresh numbers not found in the NCERT book. Full worked solutions included. These Class 8 Mathematics Chapter 10 important questions are handy for last-minute exam practice.

Last Updated: September 23, 2026

Q1 (Three-way ratio division). A prize fund of ₹7,200 is split among Gold, Silver and Bronze winners in the ratio 5 : 3 : 1. Find each winner’s share.
Solution: Total parts = 9. Gold = 5/9×7200 = ₹4,000. Silver = 3/9×7200 = ₹2,400. Bronze = 1/9×7200 = ₹800.

Q2 (Inverse proportion test). Check whether the pairs (6,40), (8,30), (12,20), (5,48) are in inverse proportion.
Solution: Products: 6×40=240, 8×30=240, 12×20=240, 5×48=240. All equal, so yes, they are in inverse proportion (constant = 240).

Q3 (Assertion–Reason). Assertion (A): If 5 taps fill a tank in 8 hours, then 8 taps will fill it in 5 hours. Reason (R): The number of taps and the time taken are directly proportional.
Solution: 5×8 = 40 tap-hours needed; with 8 taps, time = 40/8 = 5 hours, so Assertion is true. But taps and time are inversely proportional, not directly, so Reason is false.

Q4 (Combined ratio + pie chart). In a survey of 450 people, favourite fruit was Mango : Banana : Apple : Others in the ratio 5 : 3 : 3 : 4. Find the pie-chart angle for each.
Solution: Total parts = 15. Mango = 5/15×360° = 120°. Banana = 3/15×360° = 72°. Apple = 3/15×360° = 72°. Others = 4/15×360° = 96°. Check: 120+72+72+96 = 360°. ✓

Q5 (Multi-step, work and pumps). Pump A alone fills a tank in 4 hours; Pump B alone fills it in 6 hours; a leak alone would empty a full tank in 12 hours. If A, B and the leak all act together, how long to fill the tank?
Solution: Combined rate = 1/4 + 1/6 − 1/12 = 3/12 + 2/12 − 1/12 = 4/12 = 1/3 tank per hour. Time = 3 hours.

Q6 (Spot the error). A student says: “If 3 workers finish a job in 12 days, then 1 worker will finish it in 12/3 = 4 days.” Is this correct?
Solution: Incorrect. Workers and days are inversely proportional, so fewer workers should take more days, not fewer. Correct approach: 3×12 = 1×x ⇒ x = 36 days.

Q7 (Reverse ratio problem). Two numbers are in the ratio 4 : 7. If 12 is added to each number, the new ratio becomes 3 : 4. Find the original numbers.
Solution: Let the numbers be 4x and 7x. (4x+12)/(7x+12) = 3/4 ⇒ 4(4x+12) = 3(7x+12) ⇒ 16x+48 = 21x+36 ⇒ 12 = 5x ⇒ x = 2.4. Numbers = 9.6 and 16.8. Check: (9.6+12)/(16.8+12) = 21.6/28.8 = 0.75 = 3/4. ✓

Q8 (Speed-time-distance, inverse proportion). A cyclist covers a fixed route in 45 minutes at 16 km/h. At what speed must she travel to cover it in 36 minutes?
Solution: Speed and time (for fixed distance) are inversely proportional: 16 × 45 = x × 36 ⇒ x = 720/36 = 20 km/h.

Q9 (Machines and output, two-step). 15 machines produce 900 units in 6 days. How many machines are needed to produce 1,800 units in 4 days (assume each machine works at the same rate)?
Solution: 15 machines make 900 units in 6 days, i.e. 900/6 = 150 units/day with 15 machines, or 10 units/day per machine. To make 1800 units in 4 days: need 1800/4 = 450 units/day. Machines needed = 450/10 = 45 machines.

Q10 (Pie chart reverse problem). In a pie chart of monthly expenses, the “Rent” sector has angle 108° and represents ₹5,400. Find the total monthly expense and the amount spent on “Food” if its sector angle is 72°.
Solution: 108° corresponds to ₹5,400, so 1° corresponds to 5400/108 = ₹50. Total expense (360°) = 360 × 50 = ₹18,000. Food (72°) = 72 × 50 = ₹3,600.

More on This Chapter

See also: NCERT Solutions for Class 8 Maths Chapter 10, Class 8 Maths NCERT Book and the Class 8 Maths Formulas Handbook.

Revision Notes: Revision Notes for Class 8 Maths Chapter 10

Frequently Asked Questions

If a certain number of workers can complete a task in a given number of days, how can inverse proportion find how long a different number of workers would take?
The total work is expressed as a constant product of workers and days, and this constant is divided by the new number of workers to find the new number of days required.

How can you distinguish between a direct proportion problem and an inverse proportion problem when reading a word problem?
In direct proportion, both quantities increase or decrease together, such as more items costing more money, while in inverse proportion, one quantity increases as the other decreases, such as fewer days needed with more workers.

Written by Satish

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