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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 3 of 15

41. A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?

  • A. 18:11
  • B. 22:13
  • C. 23:12
  • D. 11:9

Explanation: A invests Rs. 8000 for 18 months, giving Rs. 144000 in investment-time. B invests Rs. 8000 for 4 months and Rs.

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Correct answer: 18:11

42. A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?

  • A. 1:2
  • B. 3:4
  • C. 2:5
  • D. 3:7

Explanation: Both partners invest for the full year, so their profits follow their capitals directly. The ratio is Rs. 6000:Rs. 8000 = 3:4.

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Correct answer: 3:4

43. A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?

  • A. Rs.1000
  • B. Rs.600
  • C. Rs.800
  • D. Rs.400

Explanation: A's investment-time is Rs. 2000 x 1 = Rs. 2000, B's is Rs. 3000 x 2 = Rs. 6000 and C's is Rs. 4000 x 2 = Rs.

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Correct answer: Rs.400

44. Kashif and Nadeem jointly started a business. Kashif invested three times as Nadeem did and invested his money for double time as compared to Nadeem. Nadeem earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?

  • A. Rs.16000
  • B. Rs.20000
  • C. Rs.24000
  • D. Rs.28000

Explanation: Kashif's money is three times Nadeem's and his investment time is twice Nadeem's, so Kashif's gain is 3 x 2 = 6 times Nadeem's gain.

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Correct answer: Rs.28000

45. A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?

  • A. Rs.3240
  • B. Rs.3600
  • C. Rs.3800
  • D. Rs.4200

Explanation: A first receives 10% of Rs. 9600, which is Rs. 960. The remaining Rs. 9600 - Rs. 960 = Rs.

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Correct answer: Rs.4200

46. The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?

  • A. 7 months
  • B. 10 months
  • C. 9 months
  • D. 11 months

Explanation: Profit is proportional to investment multiplied by time. P's investment-time is 7 x 5 = 35 units and Q's is 5 x t units; because the…

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Correct answer: 10 months

47. A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?

  • A. Rs.10000
  • B. Rs.12800
  • C. Rs.6000
  • D. Rs.8000

Explanation: B's share is 2/7, so A:B profit ratio is 5:2. A's investment-time is Rs. 16000 x 8 = Rs. 128000, hence B's is Rs. 128000 x 2/5 = Rs.

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Correct answer: Rs.12800

48. In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?

  • A. Rs.3250
  • B. Rs.6250
  • C. Rs.10250
  • D. Rs.11750

Explanation: With equal investment periods, profit shares are proportional to capitals. A's Rs. 200 share corresponds to Rs. 5000 capital, so B's Rs.

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Correct answer: Rs.11750

49. A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?

  • A. 9:10
  • B. 9:8
  • C. 3:4
  • D. 39:49Islamic Studies Quiz

Explanation: Profit is divided according to capital multiplied by time. A's investment units are Rs.3000 x 6 months + Rs.6000 x 6 months =…

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Correct answer: 9:8

50. A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?

  • A. 39:40
  • B. 40:39
  • C. 3:4
  • D. 4:3

Explanation: The first year's profit is divided in the ratio 300:400 = 3:4, so A receives Rs.210 x 3/7 = Rs.90.

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Correct answer: 39:40

51. A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?

  • A. 120
  • B. 180
  • C. 200
  • D. 280

Explanation: A contributes 80 cows x 7 months = 560 cow-months. B must contribute one and a half times this amount, or 560 cow-months x 3/2 = 840…

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Correct answer: 280

52. A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?

  • A. Rs.7500
  • B. Rs.7200
  • C. Rs.6000
  • D. Rs.5750

Explanation: Let A's capital be Rs.x. A contributes Rs.x x 12 months = Rs.12x-months, B contributes Rs.2x x 6 months = Rs.12x-months, and C contributes…

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Correct answer: Rs.6000

53. Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?

  • A. Rs.2400
  • B. Rs.3600
  • C. Rs.2850
  • D. Rs.2000

Explanation: Let the first investment be Rs.x, so the three investments are Rs.x, Rs.(x + 1000), and Rs.(x + 2000).

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Correct answer: Rs.2400

54. A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?

  • A. Rs.2450
  • B. Rs.3600
  • C. Rs.2500
  • D. Rs.3100

Explanation: When the profit rate rises by 7% - 5% = 2%, A's increase is two-thirds of 2% of the total capital.

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Correct answer: Rs.2500

55. Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?

  • A. 1/3 rd
  • B. 2/5 th
  • C. 2/3 rd
  • D. 1/5 th

Explanation: Using cows as the common unit, 3 horses = 5 cows, so A contributes 21 x 3 x 5/3 = 105 cow-months from horses and 15 x 2 = 30 cow-months…

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Correct answer: 1/3 rd

56. A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?

  • A. Rs.270
  • B. Rs.185
  • C. Rs.215
  • D. Rs.380

Explanation: The capital-time contributions are A: 12 horses x 8 months = 96 horse-months, B: 16 horses x 9 months = 144 horse-months, and C: 18 horses…

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Correct answer: Rs.270

57. A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.

  • A. 1750
  • B. 1900
  • C. 8600
  • D. 10300

Explanation: The capital-time values are A: Rs.6500 x 6 months = Rs.39000-months, B: Rs.8400 x 5 months = Rs.42000-months, and C: Rs.10000 x 3 months =…

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Correct answer: 1900

58. If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is:

  • A. 3:4:5
  • B. 12:15:20
  • C. 20:15:12
  • D. 6:8:10Quiz Mode Feature

Explanation: From 6A = 8B = 10C, let the common value be k. Then A = k/6, B = k/8, and C = k/10; multiplying by 120 gives the capital ratio 20:15:12.

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Correct answer: 20:15:12

59. A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?

  • A. Rs.3750
  • B. Rs.3000
  • C. Rs.3200
  • D. Rs.2160

Explanation: The capital-time contributions are A: Rs.6000 x 5 months = Rs.30000-months, B: Rs.3600 x 6 months = Rs.21600-months, and C: Rs.7500 x 3…

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Correct answer: Rs.3000

60. A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?

  • A. Rs.2400
  • B. Rs.1800
  • C. Rs.3600
  • D. Rs.6000

Explanation: A's capital-time contribution is Rs.1200 x 12 months = Rs.14400-months.

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Correct answer: Rs.2400
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