Class 8 Direct and Inverse Proportions — practice questions with answers
Direct and Inverse Proportions · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Two quantities x and y are in direct proportion when:
Axy stays constant
Bx times y stays constant
Cx + y stays constant
Dx - y stays constant
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Answer: A) xy stays constant
In direct proportion, as x increases y increases in the same ratio, so xy is a constant (k). This means y = kx.
2. If 15 metres of cloth cost 525 rupees, find the cost of 11 metres (in rupees).
A770
B425
C345
D385
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Answer: D) 385
Cost is in direct proportion to length. Per metre = 15525 = 35 rupees. For 11 metres: 11 x 35 = 385 rupees.
3. If two quantities x and y are in direct proportion, then y1x1 equals:
Ay2x2
Bx2y2
Cx2 times y2
Dx2 - y2
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Answer: A) y2x2
In direct proportion the ratio yx is constant, so y1x1=y2x2 for any two corresponding pairs.
4. Which statement is CORRECT about proportions?
AIn inverse proportion, when one quantity increases the other decreases so that their product is constant
BIn direct proportion, the product of the two quantities is constant
CIn inverse proportion, the ratio of the two quantities is constant
DDirect and inverse proportion mean the same thing
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Answer: A) In inverse proportion, when one quantity increases the other decreases so that their product is constant
Inverse proportion keeps the product constant; direct proportion keeps the ratio constant. The first statement is the correct one.
5. 6 taps can fill a tank in 4 hours. Because of a fault, only 4 taps work. By how many HOURS will the filling time increase compared to the original 4 hours?
A3
B2
C1
D4
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Answer: B) 2
Taps and time are inversely proportional. Work = 6 x 4 = 24 tap-hours. With 4 taps: 424 = 6 hours. Increase = 6 - 4 = 2 hours.