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All Free Mathematics MCQs with Answers

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1,551 questions · page 61 of 78

1201. A alone can finish a work in X days. B alone can finish the same work in X+5 days. Together, they take 6 days to complete the work. Find X

  • A. 12
  • B. 8
  • C. 10
  • D. 9

Explanation: The combined rate equation is 1/X + 1/(X+5) = 1/6. Multiplying through gives 6(2X+5) = X(X+5), so X² - 7X - 30 = 0 = (X-10)(X+3), and the…

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Correct answer: 10

1202. 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

1203. 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

1204. 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

1205. 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

1206. 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

1207. 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

1208. 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

1209. 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

1210. 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

1211. 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

1212. 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

1213. 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

1214. 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

1215. 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

1216. 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

1217. 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

1218. 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

1219. 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

1220. 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
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