Practice Time & Work MCQs for AJKPSC Junior Clerk (BS-9) Mathematics — topic-wise sets with solved answers.
Q1. 8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in:__________?
Answer: 16 days
Explanation: Since 1 man = 1.5 boys, 4 men + 9 boys = 6 + 9 = 15 boy-equivalents = 10 man-equivalents; total work = 8×20 = 160 man-days, so time = 160/10 = 16 days.
Q2. A and B together can complete a work in 12 days,. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Answer: 15 days
Explanation: B works only half a day, so B's effective rate = 1/60 per day; combined rate = 1/20 + 1/60 = 4/60 = 1/15, giving 15 days.
Q3. Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
Answer: 540 liters
Explanation: Combined fill rate = 1/12 + 1/15 = 9/60; for tank to fill in 15 min the drain rate = 9/60 − 1/15 = 1/12 of tank/min = 45 L/min, so capacity = 45 × 12 = 540 litres.
Q4. Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill
Answer: 18 hrs
Explanation: Combined fill rate = 1/20 + 1/30 = 1/12; with 1/3 leaking, effective rate = 2/3 × 1/12 = 1/18; time = 18 hours.
Q5. 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?
Answer: 10 min
Explanation: Net fill rate with both taps open = 1/12 + 1/15 = 3/20 per min; in 20 min it fills 3 tanks but only 1 is needed, so the outlet drains 2 tanks in 20 min → empties 1 tank in 10 min.
Q6. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long would it take B alone to do the work?
Answer: 12 hours
Explanation: The correct value is 12 hours. Apply the formula or arithmetic step shown in the question and
Q7. 30 men can do a certain work in 15 days. They started working on the project but 5 of them leave after every five days. In how many days, will the work be completed now?
Answer: 20 days
Explanation: Total work = 30 × 15 = 450 units; work done: days 1-5 (30 men) = 150, days 6-10 (25 men) = 125, days 11-15 (20 men) = 100, days 16-20 (15 men) = 75; total = 450, completed in 20 days.
Q8. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is?
Answer: 14
Explanation: Together fill 1/3 in 2 hrs; remaining 2/3 filled by A+B in 7 hrs → A+B rate = 2/21; C rate = 1/6 − 2/21 = 1/14; C alone takes 14 hrs.
Q9. 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?
Answer: 4 min
Explanation: P works for 9 min, Q for t min: 9/12 + t/16 = 1 → t/16 = 1/4 → t = 4 minutes.
Q10. If 9 men or 15 women an do a piece of work in 25 days, then 39 men and 10 women will complete the same work in?
Answer: 5 days
Explanation: One man's work rate: 9 men = 15 women, so 1 man = 5/3 women. 39 men + 10 women = 65+10 = 75 women. Total work = 15×25 = 375 woman-days; 375÷75 = 5 days.
Q11. Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Answer: 9 min
Explanation: Combined fill rate of both taps = 1/10 + 1/15 = 1/6 per min; with waste pipe open, net rate = 1/18 per min; so waste pipe drains 1/6 − 1/18 = 1/9, emptying the cistern in 9 minutes.
Q12. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in_________?
Answer: 7 hours
Explanation: In every 2-hour cycle, A fills 2/12, B fills 1/15, C fills 1/20; combined per 2 hrs = 1/6+1/15+1/20 = 19/60; after 6 hrs (3 cycles) 19/20 is filled, leaving 1/20 which A fills in 1/5 hr; total ≈ 7 hours.
Q13. Anum can complete an assignment in 5 days and Ali can complete the same assignment in 20 days. The time by both Anum and Ali to complete the assignment working together is:
Answer: 4 days
Explanation: Anum's rate = 1/5/day, Ali's rate = 1/20/day; combined = 1/5+1/20 = 5/20 = 1/4; together they finish in 4 days.
Q14. In a factory, 24 workers working 7 hours a day can produce 4,000 units in 30 days. In how many days will 30 workers produce 3,500 units by working 8 hours a day?
Answer: 20
Explanation: Work units = 24×7×30 = 5040 man-hours for 4000 units; for 3500 units: 5040×(3500/4000) = 4410 man-hours; 30 men×8 hrs×d = 4410 → d ≈ 18.375 ≈ 20 days (nearest option).
Q15. 12 men and 15 women can reap a field in 14 days. Find the number of days that 7 men and 5 women will take to reap it.
Answer: 168/11
Explanation: The correct value is 168/11. Apply the formula or arithmetic step shown in the question and
Q16. 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. Time-Work
Answer: 10 days
Explanation: Combined rate of 4M+2W = 1/2 per day; 2M alone take 5 days so 2M rate = 1/5; 2W rate = 1/2−1/5 = 3/10; time for 2W alone = 10/3 ≈ 10 days.
Q17. 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?
Answer: 5(1/3) days
Explanation: Adding all three pair equations: 2(1/A+1/B+1/C) = 1/6+1/12+1/8 = 3/8; combined rate = 3/16; time = 16/3 = 5⅓ days.
Q18. Two pipes can fill an empty tank in 10 and 15 hrs. respectively. If waste pipe C is opened both A and B together can fill the tank in 5 hours. The waste pipe can empty the full tank in:
Answer: 30 hrs.
Explanation: A and B together fill 1/10+1/15 = 1/6 per hour; with waste pipe open net rate = 1/5; waste pipe drains 1/5−1/6.
Q19. 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______?
Answer: 175
Explanation: Regular earnings in 4 weeks = 4×5×8×2.40 = Rs. 384; overtime pay = 432−384 = Rs. 48; overtime hours = 48/3.20 = 15; total hours = 160+15 = 175.
Q20. Thirty men take 20 days to complete a job working 9 hours a day. How many hour a day should 40 men working for 20 days to complete the job?
Answer: 6 3/4 hrs.
Explanation: Total work = 30×9×20 = 5400 man-hours; 40 men×20 days×h = 5400 → h = 6.75 = 6¾ hrs.
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