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Free Ratio and Proportion MCQs with Answers

293 Ratio and Proportion MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.

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293 questions · page 2 of 15

21. 18 cattle graze a field in 12 days. 6 cattle can graze 3 of such fields in x days. What is x?

  • A. 90
  • B. 72
  • C. 36
  • D. 108

Explanation: One field requires 18 cattle x 12 days = 216 cattle-days, so 3 fields require 3 x 216 = 648 cattle-days.

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Correct answer: 108

22. 25 men can consume 250kg of wheat in 20 days. 20 men cang consume how much wheat in 25 days?

  • A. 300
  • B. 200
  • C. 250
  • D. 350Downloading Digital Educational Resources

Explanation: The consumption rate is 250 kg ÷ (25 men x 20 days) = 250 kg ÷ 500 man-days = 0.5 kg per man-day.

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Correct answer: 250

23. In a ship the provisions are sufficient for 800 men for 50 days. How long will these be sufficient for if there would have been 200 more men?

  • A. 40
  • B. 50
  • C. 30
  • D. 56

Explanation: The provisions equal 800 men x 50 days = 40,000 man-days. For 800 + 200 = 1000 men, the duration is 40,000 man-days ÷ 1000 men = 40 days.

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Correct answer: 40

24. In a fort there is enough food sufficient for 1200 men for 10 days. How long the food would have last for if there would have been 1000 men.

  • A. 15
  • B. 12
  • C. 10
  • D. 20Finding Low Interest Personal Loans

Explanation: The food stock represents 1200 men x 10 days = 12,000 man-days. For 1000 men, it will last 12,000 man-days ÷ 1000 men = 12 days.

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Correct answer: 12

25. A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?

  • A. 2 : 3 : 4
  • B. 3 : 2 : 4
  • C. 3: 2 : 1
  • D. 3: 4 : 7

Explanation: Profit is shared according to capital multiplied by the time invested. The capital-time products are A: Rs.

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Correct answer: 3: 4 : 7

26. A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?

  • A. 4 months
  • B. 5 months
  • C. 6 months
  • D. 8 months

Explanation: A's capital-time product for 12 months is Rs. 85,000 x 12 months = 1,020,000 Rs.-months.

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Correct answer: 8 months

27. Ameen started a business investing Rs. 70,000. Rahim joined him after six months with an amount of Rs. 1,05,000 and sameer joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Ameen, Rahim and Sameer respectively, 3 years after Ameen started the business?

  • A. 7:6:10
  • B. 12:15:16
  • C. 42:45:56
  • D. Cannot be determined
  • E. None of these

Explanation: Ameen invests Rs. 70,000 for 36 months, giving Rs. 70,000 x 36 months = 2,520,000 Rs.-months. Rahim invests Rs.

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Correct answer: 12:15:16

28. A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?

  • A. Rs. 7500
  • B. Rs. 9000
  • C. Rs. 9500
  • D. Rs. 10,000
  • E. None of these

Explanation: A contributes Rs. 20,000 x 24 months = 480,000 Rs.-months, B contributes Rs.

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Correct answer: Rs. 7500

29. Sameena started a software business by investing Rs. 50,000. After six months, Nida joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Saneena's share in the profit?

  • A. Rs. 9423
  • B. Rs. 10,250
  • C. Rs. 12,500
  • D. Rs. 14,000
  • E. None of these

Explanation: Sameena's capital-time product is Rs. 50,000 x 36 months = 1,800,000 Rs.-months, while Nida's is Rs.

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Correct answer: None of these

30. Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?

  • A. Rs. 1883.78
  • B. Rs. 2380
  • C. Rs. 3690
  • D. Rs. 3864

Explanation: Profit is divided according to capital multiplied by the time invested. Kamal's investment-time is Rs. 9000 x 12 = Rs.

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Correct answer: Rs. 2380

31. A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are:

  • A. Rs. 10,500, Rs. 13,500, Rs. 16,500
  • B. Rs. 11,500, Rs. 13,000, Rs. 16,000
  • C. Rs. 11,000, Rs. 14,000, Rs. 15,500
  • D. Rs. 11,500, Rs. 12,500, Rs. 16,500

Explanation: Since all three partners invest for the same period, their profit ratio is 35000:45000:55000 = 7:9:11. The total of 27 parts is Rs.

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Correct answer: Rs. 10,500, Rs. 13,500, Rs. 16,500

32. Anees and Raees started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Raees's share is:________?

  • A. Rs. 5400
  • B. Rs. 7200
  • C. Rs. 8400
  • D. Rs. 9600

Explanation: Anees and Raees share the profit in the ratio of their capitals, 22500:35000 = 9:14. Raees therefore receives 14/23 of Rs.

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Correct answer: Rs. 8400

33. P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?

  • A. 3:4
  • B. 3:5
  • C. 15:23
  • D. 17:23
  • E. None of these

Explanation: Both partners invest for the same two years, so time cancels and the profit ratio is the capital ratio, Rs. 85000:Rs. 15000 = 17:3.

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Correct answer: None of these

34. X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?

  • A. 7
  • B. 6
  • C. 3
  • D. 4
  • E. None of these

Explanation: Let Z invest for t months. The investment-time products are Rs. 20000 x 12 = Rs. 240000, Rs. 25000 x 12 = Rs. 300000 and Rs. 30000t.

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Correct answer: None of these

35. P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?

  • A. 2 : 5
  • B. 5 : 2
  • C. 3 : 5
  • D. 1 : 1
  • E. None of these

Explanation: P's annual salary is Rs. 5000 x 12 = Rs. 60000, leaving Rs. 200000 - Rs. 60000 = Rs. 140000 to divide in the capital ratio 4:10 = 2:5.

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Correct answer: 1 : 1

36. Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?

  • A. Rs. 4500
  • B. Rs. 4800
  • C. Rs. 5250
  • D. Rs. 6150
  • E. None of these

Explanation: Rent is proportional to the number of cars multiplied by the number of days. A used 15 x 12 = 180 car-days, so the rate was Rs.

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Correct answer: Rs. 6150

37. A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?

  • A. Rs. 28000
  • B. Rs. 24000
  • C. Rs. 30000
  • D. Rs. 26000
  • E. None of these

Explanation: A's investment-time is Rs. 70000 x 12 = Rs. 840000, while B's is Rs. 120000 x 6 = Rs. 720000, so their profit ratio is 7:6.

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Correct answer: Rs. 24000

38. A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?

  • A. Rs. 300
  • B. Rs. 400
  • C. Rs. 500
  • D. Rs. 600
  • E. None of these

Explanation: The capital ratio is 8000:10000:12000 = 4:5:6. B's 5 parts equal Rs. 1500, so one part is Rs. 300; A receives Rs. 1200 and C receives Rs.

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Correct answer: Rs. 600

39. A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?

  • A. 20:23
  • B. 34:43
  • C. 32:45
  • D. 37:45

Explanation: A's investment-time is Rs. 8000 x 4 + Rs. 4000 x 8 = Rs. 64000. B's is Rs. 9000 x 6 + Rs. 6000 x 6 = Rs.

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Correct answer: 32:45

40. A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?

  • A. Rs.8000, Rs.17000
  • B. Rs.9000, Rs.16000
  • C. Rs.18000, Rs.7000
  • D. Rs.10000, Rs.15000

Explanation: A's investment-time is Rs. 10000 x 8 = Rs. 80000, and B's is Rs. 10000 x 12 = Rs. 120000, giving a profit ratio of 2:3. Out of Rs.

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Correct answer: Rs.10000, Rs.15000
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