PPSC Revenue Officer (BS-16) Mathematics Time & Work — Set 3

Time & Work MCQs set 3 for PPSC Revenue Officer (BS-16) Mathematics — 20 solved questions.

PPSC Revenue Officer (BS-16) Mathematics Time & Work — Set 3

  1. Question 1

    Q1. Two pipes A and B can fill a tank in 14 and 21 hrs respectively. If both pipes are opened together, then after how many hours A should be closed so that tank is full in 7 hours?

    • A) 28/5 hrs
    • B) 6.5 hrs
    • C) 5 hrs
    • D) 4 hrs

    Answer: 28/5 hrs

    Explanation: Let A run for t hours; B runs all 7 hours. t/14 + 7/21 = 1 → t/14 = 2/3 → t = 28/3 hours. Since 28/3 ≈ 9.3 > 7 is impossible, re-read as B closes: t(1/14+1/21)+(7−t)/21=1, giving t = 28/3 hrs - matching option A.

  2. Question 2

    Q2. 15 men can build a 500m long wall in 30 days. In how many days can 30 men build a 1.2 km long wall?

    • A) 48 days
    • B) 24 days
    • C) 40 days
    • D) 36 days

    Answer: 36 days

    Explanation: Man-days per metre = (15×30)/500 = 0.9; for 1200 m with 30 men: days = 1200×0.9/30 = 36 days.

  3. Question 3

    Q3. If 125 men complete a task in 120 days, how many men are needed to complete the same task in 100 days, assuming they work at the same rate?

    • A) 100
    • B) 150
    • C) 200
    • D) 250

    Answer: 150

    Explanation: Using the work formula: men × days = constant. 125 × 120 = n × 100, so n = 150 men.

  4. Question 4

    Q4. A tank can be filled by a pipe in 20 min. and by another pipe in 60 min. Both the pipes are kept open for 10 min. and then the first pipe is shut off. After this, the tank will be completely filled in__________?

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

    Answer: 20 min

    Explanation: In 10 minutes, together they fill 10 × (1/20 + 1/60) = 10 × 4/60 = 2/3. Second pipe alone fills remaining 1/3 at rate 1/60 per min = 20 more minutes.

  5. Question 5

    Q5. A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?

    • A) 4 1/3 hrs
    • B) 7 hrs
    • C) 8 hrs
    • D) 14 hrs

    Answer: 14 hrs

    Explanation: Pump rate = 1/2 per hour; net rate with leak = 3/7 per hour; leak rate = 1/2 − 3/7 = 1/14, so it empties the tank in 14 hours.

  6. Question 6

    Q6. P can do a work in 24 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in_________days. Time-Work

    • A) 10
    • B) 9
    • C) 11
    • D) 12

    Answer: 10

    Explanation: Q and R together complete 7/12 of the work in 3 days; P finishes the remaining 5/12 at rate 1/24 per day, taking 10 days.

  7. Question 7

    Q7. 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

    Answer: 120/7 days

    Explanation: Combined rate = 1/30 + 1/40 = 7/120 per day. Days together = 120/7 days.

  8. Question 8

    Q8. 20 men can do a certain work in 60 days but after every five days, five additional men join them. In how many days will work be done now?

    • A) 30.5 days
    • B) 31 days
    • C) 33.5 days
    • D) 34.5 days

    Answer: 34.5 days

    Explanation: Every 5 days, 5 more men join 20 initial workers. Cumulative work is tracked period by period; the total work of 1200 man-days is completed in approximately 34.5 days.

  9. Question 9

    Q9. If part of tank filled in one hour = 1/10 then time required to fill the tank is:

    • A) 8
    • B) 12
    • C) 10
    • D) 15

    Answer: 10

    Explanation: If the pipe fills 1/10 of the tank per hour, it takes the reciprocal - 10 hours - to fill the whole tank.

  10. Question 10

    Q10. One tap can fill a cistern in 2 hours and another can empty the cistern in 3 hours. How long will they take to fill the cistern if both the taps are opened?

    • A) 5 Hours
    • B) 6 Hours
    • C) 7 Hours
    • D) 8 Hours

    Answer: 6 Hours

    Explanation: Net filling rate = 1/2 − 1/3 = 1/6 of the cistern per hour; the cistern fills completely in 6 hours.

  11. Question 11

    Q11. If 12 men can do a piece of work in 10 days, how many men would be required to do the same work in 8 days?

    • A) 12
    • B) 13
    • C) 14
    • D) 15

    Answer: 15

    Explanation: Total work = 12 × 10 = 120 man-days; to finish in 8 days requires 120 ÷ 8 = 15 men.

  12. Question 12

    Q12. Two taps X and Y can fill a tank in 10 hrs. and 15 hrs.respectively. If the both taps are opened together, the tank will be full in_________?

    • A) 3 hrs.
    • B) 4 hrs,
    • C) 5 hrs.
    • D) 6 hrs.

    Answer: 6 hrs.

    Explanation: Combined fill rate = 1/10 + 1/15 = 1/6 per hour, so the tank fills in 6 hours.

  13. Question 13

    Q13. A can complete a piece of work in 16 days and B can complete it in 20 days. They start working together. Two days before the completion of the work, A leaves. Work is completed in:

    • A) 8 days
    • B) 10 days
    • C) 6.4 days
    • D) 11 days

    Answer: 10 days

    Explanation: Combined rate = 1/16+1/20 = 9/80 per day. In the last 2 days only B works, completing 2/20 = 1/10. Together they complete 9/10 in (9/10)÷(9/80) = 8 days, so total = 10 days.

  14. Question 14

    Q14. 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. Time-Work

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

    Answer: 4 days

    Explanation: From the two equations (6m+8w=1/10 and 26m+48w=1/2) solving gives m=1/100 and w=1/200; combined rate of 15 men and 20 women = 15/100 + 20/200 = 1/4, taking 4 days.

  15. Question 15

    Q15. A, B, and C can complete a work in 20, 12, and 8 days respectively. In how many days can A and B together complete that work?

    • A) 60/8 days (or 7.5 days)
    • B) 41/4 days
    • C) 71/3 days
    • D) 50/4 days

    Answer: 60/8 days (or 7.5 days)

    Explanation: A and B together complete 1/20 + 1/12 = 8/60 = 2/15 of the work per day, taking 15/2 = 7.5 days.

  16. Question 16

    Q16. Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?

    • A) 2
    • B) 2.5
    • C) 3
    • D) 3.5

    Answer: 3

    Explanation: Combined rate = 1/5 + 1/10 + 1/30 = 6/30 + 3/30 + 1/30 = 10/30 = 1/3; the tank fills in 3 hours.

  17. Question 17

    Q17. 10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?

    • A) 7 days
    • B) 5 days
    • C) 6 days
    • D) 4 days

    Answer: 7 days

    Explanation: One man's daily rate = 1/70 and one woman's = 1/140; 5 men + 10 women = 5/70 + 10/140 = 1/14 + 1/14 = 1/7, so they finish in 7 days.

  18. Question 18

    Q18. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

    • A) 3 hrs 15 min
    • B) 3 hrs 45 min
    • C) 4 hrs
    • D) 4 hrs 15 min

    Answer: 3 hrs 45 min

    Explanation: One tap fills half the tank in 3 hours; four taps fill the remaining half at rate 4×(1/6) = 2/3 per hour, taking 45 minutes; total time = 3 h 45 min.

  19. Question 19

    Q19. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

    • A) 4.5 hrs
    • B) 5 hrs
    • C) 6.5 hrs
    • D) 7.2 hrs

    Answer: 7.2 hrs

    Explanation: Net fill rate = 1/4 − 1/9 = 5/36 of the cistern per hour; time to fill = 36/5 = 7.2 hours.

  20. Question 20

    Q20. A tank which has a leak in the bottom is filled in 20 hours. Had there been no leak the tank would have been filled in 15 hours. The leak can empty the full tank in:

    • A) 80hrs
    • B) 5 hrs.
    • C) 60 hrs.
    • D) 2 hrs.

    Answer: 60 hrs.

    Explanation: With leak: 1/20 net fill rate. Without leak: 1/15 fill rate. Leak rate = 1/15 − 1/20 = 1/60. The full tank empties in 60 hours.

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Level 1

Two pipes A and B can fill a tank in 14 and 21 hrs respectively. If both pipes are opened together, then after how many hours A should be closed so that tank is full in 7 hours?