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deepshikhasingh15
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Time ended
G8 Direct and Inverse Propotions
Math quiz helps us to enhance brains neural network.
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1) 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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2) If a car covers a journey in 6 hours at a speed of 60 km/h, how long will it take at 90 km/h?
Speed × Time = Constant60 × 6 = 90 × x,x = (60 × 6) ÷ 90 = 4 hours.
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3) 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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4) The time taken to fill a tank is inversely proportional to the rate of water flow. If the tank takes 10 hours to fill at a rate of 5 liters per minute, how much time will it take at a rate of 7 liters per minute?
Let the time be x. By inverse proportion: 5 × 10 = 7 × x x = (5 × 10)/7 = 7.14 hours
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5) If 6 men can do a job in 8 days, how many men are needed to do the job in 4 days?
Men ∝ 1/Days
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6) If 2.5 kg of mangoes cost ₹225, what is the price of 4 kg?
Cost per kg = 225 / 2.5 = ₹90 4 × 90 = ₹360
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7) The volume of a gas varies directly as the temperature and inversely as the pressure. If V = 100 when T = 300 and P = 2, find V when T = 400 and P = 5.
V ∝ T/P => V = k(T/P).
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8) The pressure of a gas varies directly as the temperature and inversely as the volume. If P = 2 when T = 300 and V = 5, find P when T = 400 and V = 10.
P ∝ T/V.
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9) The number of workers needed to complete a task is inversely proportional to the number of days taken to complete the task. If 20 workers can complete a task in 25 days, how many workers are required to complete the task in 15 days?
Let the number of workers be x. By inverse proportion: 20 × 25 = x × 15 x = (20 × 25)/15 = 33.33 workers
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10) A device uses 2.4 units of electricity in 3 hours. How many units will it use in 7.5 hours?
Units ∝ Time → 2.4 / 3 = x / 7.5 → x = (2.4 × 7.5)/3 = 6 units
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11) 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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12) If 250 g of tea costs ₹90, what is the cost of 600 g?
Cost per gram = ₹90 / 250 = ₹0.36 Cost for 600 g = 600 × 0.36 = ₹216
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13) If 12 men complete a job in 18 days, how long will 8 men take?
12 × 18 = 8 × x → x = (12 × 18)/8 = 27 days
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14) A car travels from city A to city B at a speed of 60 km/h and takes 4 hours. If the speed is increased to 80 km/h, how long will the journey take?
Time ∝ 1/Speed.
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15) If it takes 5 hours to travel from City A to City B at 48 km/h, how long will it take at 80 km/h?
48 × 5 = 80 × x → x = (48 × 5)/80 = 3 hours
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16) The area of a square is directly proportional to the square of its side length. If the area of a square with side length 4 cm is 16 cm², what is the area of a square with side length 6 cm?
Let the area of the second square be x. By direct proportion: (4)²/(6)² = 16/x x = (16 × 36)/16 = 36 cm²
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17) 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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18) If x varies directly as y and z, and x = 12 when y = 2 and z = 3, find x when y = 4 and z = 5
x ∝ yz => x = kyz
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19) The cost of traveling 180 km is ₹900. What is the cost of traveling 240 km?
Cost per km = 900 / 180 = ₹5 240 × 5 = ₹1200
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20) If 12 workers finish a task in 20 days, how many workers are required to finish it in 15 days?
12 × 20 = x × 15 → x = (12 × 20) / 15 = 16 workers
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