Direct and Inverse Variations — Practice Quiz
ICSE · Class 8 · Mathematics
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Quick Quiz: Direct and Inverse Variations
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A can do a piece of work in 80 days and B in 100 days. They work together for 20 days. How much work is left?
A and B can do a piece of work in 45 days and 40 days respectively. They began the work together, and B finished the remaining work in 23 days after A left. After how many days did A leave the work?
A can do 2/3 of a work in 12 days and B can do 1/6 of the same work in 4 days. In how many days will they together complete the work?
Pipe A fills a tank in 12 minutes, pipe B fills it in 16 minutes, and pipe C empties it in 8 minutes. If all three are opened together, in how many minutes will the tank be full?
Sample Questions
If 78 men can do a work in 140 days, how many days will 42 men take to do the same work?
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260 days
This is inverse variation, so men × days is constant. 78 × 140 = 42 × d d = (78 × 140) / 42 First simplify 78/42 = 13/7. So d = 13 × 20 = 260 days. The answer is 260 days.
A and B together can finish a work in 15 days, B and C in 20 days, and C and A in 30 days. How long will all three take together?
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13 1/3 days
A + B work in 1 day = 1/15. B + C work in 1 day = 1/20. C + A work in 1 day = 1/30. Add all three: 2(A + B + C) = 1/15 + 1/20 + 1/30 = (4 + 3 + 2)/60 = 9/60 = 3/20. So A + B + C in 1 day = 3/40. Time taken = 40/3 = 13 1/3 days. So the correct answer is 13 1/3 days.
A can do 2/3 of a work in 12 days. In how many days will A complete the whole work?
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18 days
If A does 2/3 of the work in 12 days, then 1 whole work takes 12 ÷ (2/3). Divide by a fraction by multiplying by its reciprocal: 12 × 3/2 = 18. So A completes the whole work in 18 days.
A journey of 240 km costs ₹4,080. What will be the cost of a journey of 432 km?
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₹7,344
This is direct variation. Cost varies directly with distance. So 240/4080 = 432/x. Cross-multiply: 240x = 4080 × 432. Or use proportion: x = (432 × 4080)/240. Since 432/240 = 1.8, x = 4080 × 1.8 = 7344. So the cost is ₹7,344.
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