Extra Questions: Class 8 Maths Chapter 7 Proportional Reasoning-1

Practice questions beyond the textbook exercises, testing deeper understanding of ratio and proportion for Class 8 Maths Chapter 7: Proportional Reasoning-1. These Class 8 Mathematics Chapter 7 important questions are handy for last-minute exam practice.

Extra Questions: Class 8 Maths Chapter 7 Proportional Reasoning-1

1. 1 (Assertion-Reason). Assertion: 6:9 and 10:15 are in proportion. Reason: Both ratios simplify to 2:3.
   Solution: Both true, and the reason correctly explains the assertion — 6:9 = 2:3 and 10:15 = 2:3, so the two ratios are equal.
2. 2 (Numerical). A car covers 180 km in 3 hours. At the same speed, how far will it travel in 5 hours?
   Solution: Speed = 180÷3 = 60 km/h. Distance in 5 hours = 60×5 = 300 km.
3. 3 (Short Answer). Are the ratios 5:8 and 8:5 the same?
   Solution: No — order matters in a ratio. 5:8 and 8:5 are reciprocals of each other and represent different comparisons, not the same relationship.
4. 4 (Applied). Two numbers are in the ratio 3:4, and their sum is 84. Find the numbers.
   Solution: Total parts = 3+4 = 7; each part = 84÷7 = 12. The numbers are 36 and 48.
5. 5 (Assertion-Reason). Assertion: If a:b = c:d, then a:c = b:d also holds. Reason: This follows because a:b=c:d means ad=bc, which is the same condition needed for a:c=b:d.
   Solution: Both true, and the reason correctly explains the assertion — both proportions reduce to the same cross-product equation, ad=bc.
6. 6 (Numerical). A recipe needs flour and sugar in the ratio 5:2 to make a 350 g mix. Find the quantity of each.
   Solution: Total parts = 7; each part = 350÷7 = 50 g. Flour = 250 g, Sugar = 100 g.
7. 7 (Synthesis). If a:b = 2:3 and b:c = 4:5, find a:b:c.
   Solution: Make b common: a:b = 2:3 = 8:12, and b:c = 4:5 = 12:15. So a:b:c = 8:12:15.
8. 8 (Applied). A map has a scale of 1:50,000. Two towns are 8 cm apart on the map. Find the actual distance in km.
   Solution: 8×50,000 = 4,00,000 cm = 4,000 m = 4 km.
9. 9 (Short Answer). Why must both terms of a ratio be in the same unit before simplifying it?
   Solution: A ratio compares two quantities as pure numbers. If the units differ (e.g. 2 m to 50 cm), they must first be converted to a common unit (2 m = 200 cm) before the ratio (200:50 = 4:1) is meaningful.
10. 10 (Assertion-Reason). Assertion: Dividing ₹600 in the ratio 1:2:3 gives ₹100, ₹200, and ₹300. Reason: The parts must add up to the total, and since 1+2+3=6 parts, each part = ₹600÷6 = ₹100.
    Solution: Both true, and the reason correctly explains the assertion — 1×100=100, 2×100=200, 3×100=300, and these sum to ₹600.

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