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G8 Direct and Inverse Propotions
Math quiz helps us to enhance brains neural network.
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1) If 8 workers earn ₹640 in a day, how much will 15 workers earn in the same time at the same rate?
Let x = total earnings 8/640 = 15/x → x = (15 × 640)/8 = ₹1200
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2) The cost of production varies directly as the number of units produced and inversely as the efficiency of the machine. If the cost is $1000 when 500 units are produced with an efficiency of 0.8, find the cost when 800 units are produced with an efficiency of 0.9.
Cost ∝ Units/Efficiency.
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3) A cake recipe requires 3 cups of flour for 5 servings. How much flour is needed for 12 servings?
Flour ∝ Servings → 3/5 = x/12 → x = (3 × 12)/5 = 7.2 cups
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4) A model car is built at a scale of 1:20. If the model is 25 cm long, how long is the actual car?
Actual = 25 × 20 = 500 cm = 5 meters
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5) A recipe needs 300 mL of milk for 6 servings. How much milk is needed for 15 servings?
Milk ∝ Servings → 300/6 = x/15 → x = (300 × 15) / 6 = 750 mL
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6) If a car takes 2 hours to reach a place at 60 km/h, how long will it take at 90 km/h?
Speed × Time = constant → 60 × 2 = 90 × x x = 120 / 90 = 1.33 hours = 1 hour 20 minutes
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7) If 2 liters of milk are needed to prepare 8 servings of kheer, how much milk is needed for 20 servings?
Milk ∝ servings → 2/8 = x/20 → x = (2 × 20)/8 = 5 liters
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8) If 3.5 kg of apples cost ₹210, find the cost of 6 kg of apples.
Cost per kg = 210 / 3.5 = ₹60 Cost for 6 kg = 60 × 6 = ₹360
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9) The time taken to complete a task varies inversely as the number of workers. If 4 workers take 6 hours to complete the task, how many workers are needed to complete it in 3 hours?
Workers ∝ 1/Time.
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10) If the time taken to cover a fixed distance is directly proportional to the speed, find the time taken when the speed is 120 km/h if the time taken at 80 km/h is 6 hours.
Let the time be x. By direct proportion: 80 × 6 = 120 × x x = (80 × 6)/120 = 4 hours
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11) A job is done by 5 men in 20 days. How many men are required to finish it in 10 days?
Men ∝ 1/Days → 5 × 20 = x × 10 → x = 100 / 10 = 10
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12) If a bus reaches a destination in 4 hours at 45 km/h, how long will it take at 60 km/h?
45 × 4 = 60 × x → x = (45 × 4)/60 = 3 hours
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13) If 8 taps can fill a tank in 3 hours, how long would 12 taps take?
8 × 3 = 12 × x → x = (8 × 3) / 12 = 2 hours
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14) If 0.5 L of oil is required for 12 packets of snacks, how much oil is needed for 60 packets?
Oil ∝ packets → 0.5/12 = x/60 → x = (0.5 × 60)/12 = 2.5 L
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15) If 5 households consume 1500 liters of water daily, how much water will 8 households consume?
Water ∝ households → 5/1500 = 8/x → x = (1500 × 8)/5 = 2400 liters
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16) If 5 pens cost ₹75, how much would 12 pens cost, assuming direct proportion?
Cost per pen = 75/5 = ₹15 Cost for 12 pens = 12 × 15 = ₹180
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17) A water tank can be filled by 3 pipes in 4 hours. How long will it take to fill the tank if 2 more pipes are added?
Time ∝ 1/Pipes.
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18) A boy runs at 10 km/h and takes 1.5 hours to reach a park. How long will he take if he runs at 6 km/h?
10 × 1.5 = 6 × x → x = (10 × 1.5)/6 = 2.5 hours
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19) 5 machines produce 200 units in 4 hours. How long will 10 machines take?
Work is fixed → 5 × 4 = 10 × x → x = (5 × 4)/10 = 2 hours
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20) If a cyclist covers a fixed distance in 4 hours at 20 km/h, how long will it take if the speed is increased to 32 km/h?
By inverse proportion: 20 × 4 = 32 × x x = (20 × 4)/32 = 2.5 hours
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