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Proportional Reasoning-2 – Class 8 Mathematics notes, important questions and MCQs

NCERT Class 8 Mathematics, chapter 10. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Two quantities can vary directly (both increase together) or inversely (one increases as the other decreases). Recognising which one applies is the key step.

Direct proportion

x/y stays constant: x₁/y₁ = x₂/y₂.
Examples: cost and quantity, distance and fuel at fixed mileage.

Inverse proportion

x × y stays constant: x₁y₁ = x₂y₂.
Examples: workers and days to finish a job, speed and time for a fixed distance.
Time and work: if A does a job in a days, A's one-day work is 1/a.

Key terms

Direct proportion: both quantities change in the same ratio
Inverse proportion: product of the quantities stays constant
Constant of proportionality: the fixed value k in y = kx (direct) or xy = k (inverse)

Formulas

Direct: x₁/y₁ = x₂/y₂
Inverse: x₁y₁ = x₂y₂

Important questions with answers

Give one example each of direct and inverse proportion.2 marks

Direct: cost of sugar and its weight. Inverse: number of workers and days to finish a job (or speed and time for a fixed distance).

If 15 notebooks cost ₹375, how many can be bought for ₹600?3 marks

Each costs ₹25; 600/25 = 24 notebooks.

A hostel has food for 120 students for 30 days. If 30 more students join, how long will the food last? If instead 20 students leave after 10 days, how long will the remaining food last?5 marks

Total food = 120 × 30 = 3,600 student-days. With 150 students: 3,600/150 = 24 days. Second case: after 10 days, food left = 120 × 20 = 2,400 student-days for 100 students, lasting 24 more days.

Quick revision

Direct: ratio constant.
Inverse: product constant.
Speed × time = distance (fixed) is inverse.

Exam tips

Ask: "If one doubles, does the other double or halve?"
More workers → fewer days (inverse).

Practice MCQs

Cost of 5 kg rice is ₹250. Cost of 8 kg is
1. ₹400
2. ₹350
3. ₹500
4. ₹320
Show answer
Answer: (a) ₹400. ₹50 per kg (direct).
Speed and time for a fixed distance are in
1. direct proportion
2. equal
3. no relation
4. inverse proportion
Show answer
Answer: (d) inverse proportion. More speed, less time.
6 workers build a wall in 10 days. 12 workers will take
1. 20 days
2. 5 days
3. 8 days
4. 12 days
Show answer
Answer: (b) 5 days. 60/12 (inverse).
A car covers 150 km in 3 hours. At the same speed, 250 km takes
1. 4 h
2. 6 h
3. 5 h
4. 4.5 h
Show answer
Answer: (c) 5 h. 50 km/h.
6 workers build a wall in 10 days. 12 workers will take
1. 5 days
2. 20 days
3. 12 days
4. 6 days
Show answer
Answer: (a) 5 days. Inverse proportion.
15 pumps empty a tank in 8 hours. To do it in 6 hours, pumps needed are
1. 18
2. 24
3. 12
4. 20
Show answer
Answer: (d) 20. 15 × 8 = 6x ⇒ x = 20.
A does a job in 10 days, B in 15 days. Together they take
1. 5 days
2. 6 days
3. 12.5 days
4. 25 days
Show answer
Answer: (b) 6 days. 1/10 + 1/15 = 1/6.
A car covers 240 km in 4 hours. At the same speed, time for 420 km is
1. 6 h
2. 5.5 h
3. 8 h
4. 7 h
Show answer
Answer: (d) 7 h. 60 km/h.

All chapters of Class 8 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.