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Free Arithmetic MCQs with Answers

1,060 Arithmetic MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Arithmetic applies numerical operations to percentages, ratios, proportions, profit and loss, averages, and practical rate problems. Questions also involve time, speed and distance, and time and work, requiring careful use of units, direct and inverse relationships, weighted values, and work-rate methods rather than algebraic manipulation.

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1,060 questions · page 29 of 53

561. 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

562. 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

563. 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

564. 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

565. 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

566. 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

567. 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

568. 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

569. 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

570. 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

571. 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

572. 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

573. 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

574. 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

575. 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

576. 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

577. 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

578. 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

579. 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

580. 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
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