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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 44 of 53

861. P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?

  • A. 7
  • B. 8
  • C. 9
  • D. 10

Explanation: The rates of P+Q, Q+R, and P+Q+R are 1/8, 1/12, and 1/6 work per day. Q's rate is 1/8 + 1/12 - 1/6 = 1/24, so P+R's rate is 1/6 - 1/24 =…

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Correct answer: 8

862. P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in__________?

  • A. 30 days
  • B. 25 days
  • C. 20 days
  • D. 15 days

Explanation: Let Q's rate be q and R's rate be 1/50. Since P can do the work in the same time as Q and R together, P's rate is q + 1/50.

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Correct answer: 25 days

863. A leak in the bottom of a tank can empty the full tank in 6 hrs. An inlet pipe fills water at the rate of 4 lit. a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hrs. The capacity of the tank in liters is_________?

  • A. 5,750 litres
  • B. 5,760 litres
  • C. 6,890 litres
  • D. None of these

Explanation: Let the tank capacity be V litres. The leak removes V/6 litres per hour, while the inlet supplies 4 litres per minute = 240 litres per…

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Correct answer: 5,760 litres

864. A tap can fill a tank in 32 min. and another can empty it in 16 min. If the tank is already half full and both the tanks are opened together, the tank will be_________?

  • A. 12 min
  • B. 14 min
  • C. 16 min
  • D. 20 min

Explanation: The filling rate is 1/32 tank per minute and the emptying rate is 1/16 tank per minute, so the net rate is 1/32 - 2/32 = -1/32 tank per…

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Correct answer: 16 min

865. A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. A alone can do the work in__________?

  • A. 20 days
  • B. 30 days
  • C. 40 days
  • D. none of these

Explanation: The pair rates are A+B = 1/12, B+C = 1/15, and C+A = 1/20. Adding them gives 2(A+B+C) = 1/12 + 1/15 + 1/20 = 1/5, so the total rate is…

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Correct answer: 30 days

866. A can lay a railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in_________?

  • A. 4
  • B. 9.6
  • C. 9
  • D. 10

Explanation: A's rate is 1/16 and B's rate is 1/12, so their combined rate is 7/48 work per day.

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Correct answer: 9.6

867. If 10 bulls can plough 20 identical fields in 3 days working 10 hours a day, then in how many days can 30 bulls plough 32 same identical fields working 8 hours a day?

  • A. 2
  • B. 8
  • C. 10
  • D. 12

Explanation: The original labour is 10 bulls x 3 days x 10 hours = 300 bull-hours for 20 fields, or 15 bull-hours per field.

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Correct answer: 2

868. P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in________days if all of them are working together.

  • A. 2
  • B. 3 3⁄7
  • C. 4 ¼
  • D. 5Election Officer Mcqs

Explanation: Their combined daily rate is 1/24 + 1/6 + 1/12 = 1/24 + 4/24 + 2/24 = 7/24 work per day.

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Correct answer: 3 3⁄7

869. Two pipes P and Q can fill a cistern in 12 minutes and 16 minutes respectively. Simultaneously both the pipes are opened together, then after how much time Q should be closed so that the tank is full in 9 min ?

  • A. 2 min
  • B. 3 min
  • C. 4 min
  • D. 5 min

Explanation: If Q is closed after t minutes, P works for all 9 minutes and Q works for t minutes.

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Correct answer: 4 min

870. A can do a certain job in 12 days. B is 60% more efficient than A. The number of days it takes for B to do the same piece of work, is:_________?

  • A. 12/6 days
  • B. 15/2 days
  • C. 23 days
  • D. 34 days

Explanation: A's rate is 1/12 work per day. B is 60% more efficient, so B's rate is 1.6 x 1/12 = 1/7.5 work per day, and B's time is 12/1.6 = 7.5 days…

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Correct answer: 15/2 days

871. A can do piece of work in 30 days while B can do it in 40 days. In how many days can A and B working together do it ?

  • A. 70 days
  • B. 120/7 days
  • C. 50 days
  • D. 45 days

Explanation: A's rate is 1/30 work per day and B's rate is 1/40 work per day, so together their rate is 1/30 + 1/40 = 7/120 work per day.

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Correct answer: 120/7 days

872. A and B can do a piece of work in 21 and 24 days respectively.They start the work together and after some days, A leaves and B completes the rest of the task in 9 days. After how many days did A leave?

  • A. 5
  • B. 6
  • C. 7
  • D. 8

Explanation: B completes 9/24 = 3/8 of the work in 9 days, so A and B together complete 5/8 of the work.

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Correct answer: 7

873. A,B,C, can do a work in 8,14,16 days respectively. A does the work for the first 2 days. B continues from it and finishes 2/3rd of the remaining work. C finishes the remaining work. How many days would have taken to complete the work?

  • A. 13
  • B. 11
  • C. 12
  • D. 15

Explanation: A completes 2 × 1/8 = 1/4 of the work, leaving 3/4; B then completes 2/3 × 3/4 = 1/2, leaving 1/4.

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Correct answer: 13

874. If 6 men working together can complete 50 identical tasks in 4 hours then how many such identical tasks can be completed if 10 men are working together for 6 hours?

  • A. 20
  • B. 25
  • C. 125
  • D. 60

Explanation: The number of tasks is proportional to the number of men and working hours, so tasks = 50 × (10 men × 6 hours) ÷ (6 men × 4 hours) = 125…

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Correct answer: 125

875. P works twice as fast as Q. If Q alone can complete a work in 12 days, P and Q can finish the work in________days

  • A. 1
  • B. 2
  • C. 3
  • D. 4

Explanation: Q's rate is 1/12 work per day, and P works twice as fast, so P's rate is 2/12 = 1/6 work per day.

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Correct answer: 4

876. P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?

  • A. 9
  • B. 11
  • C. 23
  • D. 13

Explanation: P's rate is 1/23 work per day; since P is 30% more efficient, Q's rate is 1/1.3 of P's rate = 10/299 work per day.

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Correct answer: 13

877. 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in_______days.

  • A. 4 days
  • B. 6 days
  • C. 2 days
  • D. 8 days

Explanation: The first group represents 10 × (6m + 8w) man-woman units, while the second represents 2 × (26m + 48w); equating them gives 60m + 80w =…

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Correct answer: 4 days

878. A cistern has two taps which fill it in 12 min. and 15 min.respectively There is one outlet pipe in the cistern. When all the taps & pipe are opened, the empty cistern is full in 20 min. How long will the waste pipe (outlet) take to empty the full cistern ?

  • A. 10 min
  • B. 20 min
  • C. 30 min
  • D. 40 min

Explanation: The two inlet taps fill at 1/12 + 1/15 = 3/20 cistern per minute, while the net rate with the outlet open is 1/20 cistern per minute.

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Correct answer: 10 min

879. To fill a cistern, pipes P, Q & R take 20, 15 & 12 minutes respectively. The time in minutes that the three pipes together will take to fill the cistern is:__________?

  • A. 5 min
  • B. 10 min
  • C. 15 min
  • D. 20 min

Explanation: The combined filling rate is 1/20 + 1/15 + 1/12 = 3/60 + 4/60 + 5/60 = 12/60 = 1/5 cistern per minute.

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Correct answer: 5 min

880. A alone can finish a work in 10 days and B alone can do it in 15 days. If they work together and finish, then out of a total wages of Rs.75. A will get:___________?

  • A. 35 Rs.
  • B. 40 Rs.
  • C. 45 Rs.
  • D. None of these

Explanation: A and B have rates 1/10 and 1/15 work per day, whose ratio is 3:2, so A deserves 3/5 of the wages. A's share is (3/5) × Rs.75 = Rs.45.

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Correct answer: 45 Rs.
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