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Proportional Reasoning-1 – Class 8 Mathematics notes, important questions and MCQs

NCERT Class 8 Mathematics, chapter 7. Notes, key terms, important questions with answers and MCQs.

Chapter overview

A ratio compares two quantities of the same kind. When two ratios are equal, the quantities are in proportion, which helps solve many daily-life problems.

Ratio

a : b = a/b; simplify by dividing by the HCF (12 : 18 = 2 : 3).
Both quantities must be in the same unit before comparing.
Dividing an amount in a ratio a : b: shares are a/(a + b) and b/(a + b) of the total.

Proportion and unitary method

a : b = c : d means a × d = b × c (product of extremes = product of means).
Unitary method: find the value of one unit, then multiply.
Scale drawings and maps use proportion (1 cm : 5 km).

Key terms

Ratio: comparison of two quantities by division
Proportion: equality of two ratios
Unitary method: finding the value of one unit first and then of the required number of units

Formulas

a : b = c : d ⇔ ad = bc
Share of A = Total × a/(a + b)

Important questions with answers

Are 4 : 6 and 10 : 15 in proportion?2 marks

4/6 = 2/3 and 10/15 = 2/3, so yes (also 4 × 15 = 6 × 10 = 60).

A map has a scale 1 : 50,000. Two towns are 6 cm apart on the map. Find the actual distance.3 marks

6 × 50,000 cm = 3,00,000 cm = 3 km.

A recipe for 4 people needs 300 g of rice and 150 g of dal. How much of each is needed for 10 people? If rice costs ₹60 per kg and dal ₹120 per kg, find the cost for 10 people.5 marks

Factor = 10/4 = 2.5. Rice = 300 × 2.5 = 750 g; dal = 150 × 2.5 = 375 g. Cost: rice 0.75 × 60 = ₹45; dal 0.375 × 120 = ₹45; total ₹90.

Quick revision

Ratios have no units.
Extremes × extremes = means × means.
Unitary method: one, then many.

Exam tips

Convert units first: 50 cm : 2 m = 50 : 200 = 1 : 4.
In map questions, multiply the map length by the scale value.

Practice MCQs

The ratio 15 : 25 in simplest form is
1. 5 : 3
2. 3 : 5
3. 15 : 25
4. 1 : 5
Show answer
Answer: (b) 3 : 5. Divide by 5.
If 4 pens cost ₹40, one pen costs
1. ₹4
2. ₹8
3. ₹10
4. ₹160
Show answer
Answer: (c) ₹10. 40 ÷ 4.
Are 3 : 4 and 12 : 16 in proportion?
1. yes
2. no
3. only sometimes
4. cannot say
Show answer
Answer: (a) yes. 3 × 16 = 4 × 12.
₹600 divided in the ratio 2 : 3 gives the larger share
1. ₹240
2. ₹400
3. ₹300
4. ₹360
Show answer
Answer: (d) ₹360. 600 × 3/5.
If 5 pens cost ₹60, 8 pens cost
1. ₹80
2. ₹96
3. ₹100
4. ₹48
Show answer
Answer: (b) ₹96. ₹12 each.
On a map 1 cm = 25 km. Two towns 6.4 cm apart are actually
1. 160 km
2. 180 km
3. 64 km
4. 150 km
Show answer
Answer: (a) 160 km. 6.4 × 25.
If x : 6 = 10 : 15, then x =
1. 2.5
2. 9
3. 5
4. 4
Show answer
Answer: (d) 4. 15x = 60.
Divide ₹1,200 between A and B in the ratio 3 : 5. B gets
1. ₹450
2. ₹720
3. ₹750
4. ₹500
Show answer
Answer: (c) ₹750. 5/8 × 1200.

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.