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All Free Mathematics MCQs with Answers

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1,551 questions · page 62 of 78

1221. 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.

1222. 2 men and 12 women can finish a job in 4 days. 4 men and 6 women can do the same job in 5 days. Find the time taken by 1 man and 1 woman to complete the job.

  • A. 30 days
  • B. 25 days
  • C. 24 days
  • D. 20 days

Explanation: Equalising the total work gives 4(2m + 12w) = 5(4m + 6w), so 8m + 48w = 20m + 30w and m = 3w/2.

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Correct answer: 24 days

1223. Bilal can do a work in 15 days and Jalal in 12 days. If they work on it together for 4 days, the fraction of work that is left is________?

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

Explanation: Their combined rate is 1/15 + 1/12 = 3/20 work per day, so in 4 days they complete 4 × 3/20 = 3/5 of the work.

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Correct answer: 2/5

1224. A and B can finish a piece of work in 20 days .B and C in 30 days and C and A in 40 days. In how many days will A alone finish the job?

  • A. 48
  • B. 34(2/7)
  • C. 44
  • D. 45

Explanation: Using pairwise rates, 2A = (A+B) + (A+C) - (B+C) = 1/20 + 1/40 - 1/30 = 1/24 work per day, so A's rate is 1/48 work per day.

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Correct answer: 48

1225. P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?

  • A. 10
  • B. 8
  • C. 18
  • D. 19

Explanation: The rate of all three together is [(1/30) + (1/24) + (1/20)] ÷ 2 = 1/16 work per day, so in 10 days they complete 5/8 and leave 3/8.

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Correct answer: 18

1226. A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in_______days.

  • A. 5 5⁄11
  • B. 4 5⁄11
  • C. 6 4⁄11
  • D. 6 5⁄11

Explanation: A completes 12 days × 8 hours = 96 hours of work, so A's hourly rate is 1/96 work per hour; B's is 1/(8 × 10) = 1/80 work per hour.

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Correct answer: 5 5⁄11

1227. A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?

  • A. Rs. 380
  • B. Rs. 600
  • C. Rs. 420
  • D. Rs. 400Educational Resources

Explanation: A and B together work at 1/6 + 1/8 = 7/24 of the job per day, so in 3 days they complete 21/24 = 7/8 and C completes the remaining 1/8.

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Correct answer: Rs. 400Educational Resources

1228. If two pipes function together, the cistern will be filled in 6 hrs. One pipe fills the cistern 5 hrs. faster than the other. How many hours it take the second pipe to fill the cistern?

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

Explanation: Let the slower pipe take t hours, so the faster takes t - 5 hours. Since together they fill 1/6 cistern per hour, 1/t + 1/(t - 5) = 1/6…

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Correct answer: 15 hrs

1229. Two pipes can fill a tank in 10 hrs. and 12 hrs. respectively while a third pipe empties the full tank in 20 hrs. If all the three pipes operate together , in how much time the tank will be filled ?

  • A. 7.5 hrs
  • B. 5 hrs
  • C. 7 hrs
  • D. None of these

Explanation: The net rate is 1/10 + 1/12 - 1/20 = 6/60 + 5/60 - 3/60 = 8/60 = 2/15 tank per hour.

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Correct answer: 7.5 hrs

1230. A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately. If A begins first, in how many days the work will be completed ?

  • A. 42/4 days
  • B. 41/4 days
  • C. 55 days
  • D. None of these

Explanation: In each two-day cycle, A and B complete 1/9 + 1/12 = 7/36 of the work. After four cycles, 28/36 = 7/9 is complete; A then works on day 9…

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Correct answer: 41/4 days

1231. 4 men and 2 woman can complete a work in 2 days. If 2 men alone take 5 days to complete the work, find the time taken by 2 women alone to complete the work.

  • A. 15 days
  • B. 10 days
  • C. 8 days
  • D. 20 days

Explanation: The complete work rate of 4 men and 2 women is 1/2 work per day. Two men complete 1/5 work per day, so 4 men complete 2/5 work per day…

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Correct answer: 10 days

1232. B can work 3 times faster than A. They work together on a task and complete it in a day. How long does it take for B alone to complete the task?

  • A. 32 hours
  • B. 48 hours
  • C. 3 days
  • D. 4 days

Explanation: If A works at x work per day, B works at 3x work per day, so together they work at 4x = 1 work per day.

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Correct answer: 32 hours

1233. A and B together take 6 days to complete a task. B and C together take 12 days to complete the same task. A and C together take 8 days to complete it. If A, B and C are working together, how long does it take for them to complete the task?

  • A. 4(2/3) days
  • B. 4 days
  • C. 5(1/3) days
  • D. 1(1/3) days

Explanation: The three pair rates are 1/6, 1/12 and 1/8 work per day. Their sum is 3/8 work per day, which counts each person's rate twice, so the…

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Correct answer: 5(1/3) days

1234. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last ?

  • A. 6 days
  • B. 10 days
  • C. 15 days
  • D. 20 days

Explanation: X completes 4 x 1/20 = 1/5 of the work in the first 4 days, leaving 4/5 of the work.

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Correct answer: 10 days

1235. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman ?

  • A. 3 : 4
  • B. 4 : 3
  • C. 5 : 3
  • D. Data inadequate

Explanation: The same work equals 20 women x 16 days = 320 woman-days and 16 men x 15 days = 240 man-days.

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Correct answer: 4 : 3

1236. A and B can do a piece of work in 72 days; B and C can do it in 120 days; A and C can do it in 90 days. In what time can A alone do it ?

  • A. 80 days
  • B. 100 days
  • C. 120 days
  • D. 150 days

Explanation: Using pair rates, A's rate is (AB + AC - BC)/2 = (1/72 + 1/90 - 1/120)/2 = (1/60)/2 = 1/120 work per day.

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Correct answer: 120 days

1237. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in___________?

  • A. 8 days
  • B. 10 days
  • C. 12 days
  • D. 15 days

Explanation: Together A and B complete 1/15 + 1/10 = 1/6 work per day, so in 2 days they complete 1/3 of the work.

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Correct answer: 12 days

1238. A can do a certain work-in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in_________?

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

Explanation: The condition says A's rate equals B plus C's rate. Since A and B together work at 1/10 work per day and C works at 1/50 work per day…

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Correct answer: 25 days

1239. In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for______?

  • A. 160
  • B. 175
  • C. 180
  • D. 195

Explanation: A regular four-week schedule has 5 x 8 x 4 = 160 regular hours, earning 160 x Rs. 2.40 = Rs. 384. The remaining Rs. 432 - Rs. 384 = Rs.

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Correct answer: 175

1240. An officer was appointed on maximum daily wages on contract money of Rs. 4956. But on being absent for some days, he was paid only Rs. 3894. For how many days was he absent?

  • A. 3
  • B. 4
  • C. 5
  • D. 6

Explanation: The loss in wages equals the number of absent days multiplied by the daily wage: Rs. 4956 - Rs. 3894 = Rs. 1062. The daily wage is Rs.

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Correct answer: 3
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