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Maths Quiz for Class 8 Direct and Inverse Proportions |
In this post, we are providing 20 online maths quiz
questions for class 8 direct and inverse proportions. Online maths quiz will
take around 20 minutes to complete it.
Question 1: The cost of 5 pens is ₹ 75. Find the cost of 8 pens of the same type.
A) ₹ 100
B) ₹ 110
C) ₹ 120
D) ₹ 130
Explanation: The cost of 5 pens = ₹ 75. Then the cost of 1 pen = ₹ 75 ÷ 5 = ₹ 15. Therefore, the cost of 8 pens = ₹ 15 × 8 = ₹ 120.
Question 2: If the cost of 3 kg of sugar is ₹ 135, then find the cost of 5 kg of sugar.
A) ₹ 225
B) ₹ 215
C) ₹ 205
D) ₹ 235
Explanation: The cost of 3 kg of sugar = ₹ 135. Then the cost of 1 kg of sugar = ₹ 135 ÷ 3 = ₹ 45. Therefore, the cost of 5 kg of sugar = ₹ 45 × 5 = ₹ 225.
Question 3: If a bus covers a distance of 240 km in 6 hours, then how long will it take to cover 160 km at the same speed?
A) 4 hours
B) 3 hours
C) 2 hours
D) 5 hours
Explanation: Let the required time be x hours. Since the distance and time are directly proportional, 240/6 = 160/x => 240x = 960 => x = 960/240 => x = 4 hours
Question 4: If a car covers 420 km in 7 hours, then find the distance travelled by the car in 5 hours at the same speed.
A) 310 km
B) 300 km
C) 320 km
D) 330 km
Explanation: Let the required distance be x km. Since the distance and time are directly proportional, 420/7 = x/5 => 7x = 2100 => x = 2100/7 => x = 300 km
Question 5: A train travels at uniform speed and covers 140 km in 2 hours. How far will it travel in 4 ½ hours?
A) 305 km
B) 315 km
C) 325 km
D) 335 km
Explanation: Let the required distance be x km. Since the distance and time are directly proportional, 140/2 = x/(9/2) => 2x = 140 × 9/2 => 2x = 70 × 9 => x = 70 × 9/2 => x = 35 × 9 => x = 315 km
Question 6: 125 books of the same size are packed in 5 boxes. How many such boxes are needed to pack 225 similar books?
A) 7 boxes
B) 8 boxes
C) 9 boxes
D) 10 boxes
Explanation: For more books, more boxes will be required. So, books and boxes are in direct proportion. Therefore, 125/5 = 225/x => 125x = 225 × 5 => x = 225 × 5/125 => x = 225 × 1/25 => x = 225/25 = > x = 9 boxes
Question 7: A 10 m long pole casts a shadow of length 2.5 m. At the same time, another pole casts a shadow of length 7.5 m. Find the length of the second pole.
A) 20 m
B) 30 m
C) 35 m
D) 40 m
Explanation: The length of the pole and the length of the shadow are in direct proportion. Therefore, 10/2.5 = x/7.5 => 2.5x = 10 × 7.5 => 2.5x = 75 => x = 75/2.5 => x = 750/25 => x = 30 m
Question 8: The wage of a labourer is ₹ 4200 for one week. If he works for 3 days, how much money will he earn?
A) ₹ 2400
B) ₹ 600
C) ₹ 1200
D) ₹ 1800
Explanation: More days of work, more wage will be earned. So, this is a case of direct proportion. 4200/7 = x/3 => 7x = 4200 × 3 => x = 4200 × 3/7 => x = 600 × 3 => x = ₹ 1800
Question 9: If a dozen bananas cost ₹ 60, then how many bananas can be bought for ₹ 35?
A) 7 bananas
B) 6 bananas
C) 5 bananas
D) 8 bananas
Explanation: More bananas more cost means the number of bananas and its cost are directly proportional. Therefore, 60/12 = 35/x => 60x = 420 => x = 420/60 => x = 7 bananas
Question 10: In a factory, an automatic machine fills 1000 milk bottles in 4 hours. How many such bottles can be filled in 10 hours by the machine?
A) 2000 bottles
B) 2200 bottles
C) 2500 bottles
D) 2600 bottles
Explanation: As the number of hours increases, the numbers of bottles filled will be increases. So, they are in direct proportion. Thus, 1000/4 = x/10 => 4x = 10000 => x = 10000/4 => x = 2500 bottles
Question 11: If 8 men can finish a work in 6 days, how long will 6 men take to finish the same work?
A) 7 days
B) 8 days
C) 9 days
D) 6 days
Explanation: For more men, less number of days is required to finish the work. So, this is the case of inverse proportion. 8 men can finish a work in 6 days. 1 man can finish a work in 6 × 8 = 48 days. Now, 6 men can finish a work in 48/6 = 8 days
Question 12: Five similar taps can fill a tank in 4 hours. If only 2 taps are open, how long will it take to fill the tank?
A) 8 hours
B) 10 hours
C) 12 hours
D) 15 hours
Explanation: This is a case of inverse proportion. 5 taps can fill a tank in 4 hours. 1 tap can fill the tank in 4 × 5 = 20 hours. So, 2 taps can fill the tank in 20/2 = 10 hours.
Question 13: In a hostel, 45 students have provisions for 30 days. How long will the provisions last if 18 students left the hostel?
A) 50 days
B) 40 days
C) 45 days
D) 55 days
Explanation: Number of remaining students if 18 students left the hostel = 45 – 18 = 27 students. If provisions are used by 45 students, it is sufficient for 30 days. If provisions are used by 1 student, it is sufficient for 30 × 45 days. If provisions are used by 27 students, it is sufficient for 30 × 45/27 = 50 days.
Question 14: A pond can be dug by 64 men in 30 days. If there are only 24 men, how long will they take to complete the work?
A) 50 days
B) 60 days
C) 70 days
D) 80 days
Explanation: The pond can be dug by 64 men in 30 days. The pond can be dug by 1 man in 30 × 64 days. The pond can be dug by 24 men in 30 × 64/24 = 80 days.
Question 15: A contractor employs 56 workers to build a bridge and agrees to get the work done in 45 days. But the government authority wants the work to be completed in 30 days. How many more workers should he employ?
A) 38 workers
B) 32 workers
C) 28 workers
D) 24 workers
Explanation: To complete the work in 45 days, the number of workers required is 56. To complete the work in 1 day, the number of workers required is 56 × 45. So, to complete the work in 30 days, the number of workers required is 56 × 45/30 = 84 workers. Number of more workers to be employed = 84 – 56 = 28
Question 16: Rohan can do a piece of work in 6 days and Neha can do the same work in 12 days. How many days will they take to do the work together?
A) 3 days
B) 4 days
C) 5 days
D) 2 days
Explanation: Rohan can do a piece of work in 6 days. One day’s work of Rohan = 1/6. Neha can do the same piece of work in 12 days. One day’s work of Neha = 1/12. One day’s work of Rohan and Neha = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = ¼. Therefore, they well complete the work in 4 days working together.
Question 17: A and B can do a piece of work in 6 days working together. If A can do the work in 10 days working alone, then how many days will B take to do the work alone?
A) 15 days
B) 12 days
C) 8 days
D) 16 days
Explanation: (A + B) can do the work in 6 days. (A + B)’s one day’s work = 1/6. A alone can do the work in 10 days. A’s one day’s work = 1/10. B’s one day’s work = 1/6 – 1/10 = (5 – 3)/30 = 2/30 = 1/15. So, B can finish the work in 15 days working alone.
Question 18: Two taps A and B can together fill an empty tank in 12 hours. Tap A alone can fill the tank in 20 hours. Find the time taken by tap B alone to fill the tank.
A) 24 hours
B) 25 hours
C) 30 hours
D) 40 hours
Explanation: Time taken by taps A and B to fill the empty tank = 12 hours. In 1 hour, taps A and B will fill 1/12 of the tank. Time taken by tap A to fill the empty tank = 20 hours. In 1 hour, tap A will fill 1/20 of the tank. In 1 hour, tap B will fill (1/12 – 1/20) = 1/30 of the tank. So, the time taken by B to fill the tank is 30 hours.
Question 19: Three pipes A, B and C can fill an empty tank in 15 hours, 10 hours and 6 hours, respectively. In how much time will the tank be filled if all the three pipes are opened together?
A) 2 hours
B) 3 hours
C) 4 hours
D) 5 hours
Explanation: Three pipes A, B and C can fill an empty tank in 15 hours, 10 hours and 6 hours. In 1 hour, pipes A, B and C will fill 1/15, 1/10 and 1/6 part of the tank. In 1 hour, pipes A, B and C will fill (1/15 + 1/10 + 1/6) = 1/3 part of the tank. Therefore, the tanks will be filled by pipes A, B and C in 3 hours.
Question 20: 4 men or 5 women can earn ₹ 1500 in a day, find the total earnings of 11 men and 12 women of one day.
A) ₹ 7750
B) ₹ 7720
C) ₹ 7725
D) ₹ 7775
Explanation: The earnings of 4 men = ₹ 1500. The earnings of 1 man = ₹ 1500 ÷ 4 = ₹ 375. The earnings of 5 women = ₹ 1500. The earnings of 1 woman = ₹ 1500 ÷ 5 = ₹ 300. The total earnings of 11 men and 12 women = ₹ 375 × 11 + ₹ 300 × 12 = ₹ 4125 + ₹ 3600 = ₹ 7725
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