Mathematics carries the highest weight in AISSEE — 150 of 300 marks in Class 6 and 200 of 400 marks in Class 9 — and it is also a key section of the RMS CET. Practise these 10 MCQs on Direct and Inverse Proportion, then check your answers and step-by-step solutions in the answer key at the end.
Quick facts: AISSEE 2027 will be held on Sunday, 31 January 2027. There is no negative marking, so attempt every question. Online applications are open until 2 December 2026 on exams.nta.nic.in/sainik-school-society.
Practice Questions
Q1. If 4 kg of sugar costs ₹60, what is the cost of 9 kg? (direct proportion)
(A) ₹135
(B) ₹140
(C) ₹150
(D) ₹69
Q2. 6 taps fill a tank in 10 hours. How long will 4 taps take? (inverse proportion)
(A) 20/3 hours
(B) 10 hours
(C) 15 hours
(D) 17 hours
Q3. The number of articles bought and the total cost are in ________ proportion.
(A) inverse
(B) no
(C) direct
(D) reverse
Q4. If 5 kg of sugar costs ₹40, what is the cost of 8 kg? (direct proportion)
(A) ₹25
(B) ₹64
(C) ₹72
(D) ₹48
Q5. 20 taps fill a tank in 6 hours. How long will 10 taps take? (inverse proportion)
(A) 3 hours
(B) 6 hours
(C) 12 hours
(D) 14 hours
Q6. If 6 kg of sugar costs ₹90, what is the cost of 10 kg? (direct proportion)
(A) ₹54
(B) ₹150
(C) ₹165
(D) ₹100
Q7. 8 taps fill a tank in 9 hours. How long will 12 taps take? (inverse proportion)
(A) 27/2 hours
(B) 6 hours
(C) 9 hours
(D) 8 hours
Q8. The number of workers and days needed to finish a job are in ________ proportion.
(A) direct
(B) equal
(C) no
(D) inverse
Q9. If 3 kg of sugar costs ₹45, what is the cost of 7 kg? (direct proportion)
(A) ₹105
(B) ₹110
(C) ₹120
(D) ₹52
Q10. 12 taps fill a tank in 10 hours. How long will 8 taps take? (inverse proportion)
(A) 20/3 hours
(B) 10 hours
(C) 17 hours
(D) 15 hours
Answer Key with Explanations
(A) ₹135 — Cost varies directly: 60/4 × 9 = ₹135.
(C) 15 hours — Fewer taps take more time: 6×10/4 = 15 hours.
(C) direct — More articles cost more money: direct proportion.
(B) ₹64 — Cost varies directly: 40/5 × 8 = ₹64.
(C) 12 hours — Fewer taps take more time: 20×6/10 = 12 hours.
(B) ₹150 — Cost varies directly: 90/6 × 10 = ₹150.
(B) 6 hours — More taps, less time: 8×9/12 = 6 hours.
(D) inverse — More workers take fewer days: inverse proportion.
(A) ₹105 — Cost varies directly: 45/3 × 7 = ₹105.
(D) 15 hours — Fewer taps take more time: 12×10/8 = 15 hours.
How did you score?
9–10 correct: excellent — move on to a full-length mock test. 6–8: good — revise the explanations of the questions you missed. Below 6: study this topic again from your NCERT book and retry these questions after two days.
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