Level 1
Time & Work MCQs set 2 for Balochistan Police Sub Inspector (BS-14) Mathematics — 20 solved questions.
Q1. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Answer: 35 hrs
Explanation: Let A's rate = r; B = 2r, C = 4r; combined 7r = 1/5 → r = 1/35; A alone takes 35 hours.
Q2. Pipes P and Q would fill a cistern 18 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in 12 minutes?
Answer: After 9 mins
Explanation: Q works all 12 min filling 12/24 = 1/2; P works t min filling t/18; t/18+1/2 = 1 → t = 9 minutes.
Q3. 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?
Answer: 7
Explanation: B completes 9/24 = 3/8 alone; remaining 5/8 done together at rate 1/21+1/24 = 15/168; time = (5/8)/(15/168) = 7 days.
Q4. P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
Answer: 9(3/5) days
Explanation: 1/P+1/Q+1/R = 1/4; 1/16+1/12+1/R = 1/4 → 1/R = 5/48; R alone takes 48/5 = 9⅗ days.
Q5. If 25 men can eat 150 kg of wheat in 30 days then 45 men can eat 450 kg of wheat in how many days?
Answer: 50 days
Explanation: Rate = 150 kg/(25×30) man-days; for 45 men eating 450 kg: days = 450×25×30/(150×45) = 50 days.
Q6. A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
Answer: 28 hours
Explanation: Let C's rate = x, then B = 2x and A = 4x; combined rate 7x fills in 8 hours so x = 1/56, and B alone (rate 2x = 1/28) takes 28 hours.
Q7. A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Answer: 6 min. to empty
Explanation: Pipe B empties faster than A fills; net drain rate = 1/6 − 1/10 = 1/15 of the tank per minute. To empty 2/5 of the tank takes (2/5) × 15 = 6 minutes.
Q8. A can do a piece of work in 6 days and B can do the same work in 12 days. How long will it take if A and B work together?
Answer: 4
Explanation: Combined work rate = 1/6 + 1/12 = 1/4 per day, so together they finish the work in 4 days.
Q9. If 6 men can make 10 sofas in 2 days, then 8 men can make 8 sofas in__________?
Answer: 1.2 days
Explanation: Total work = 6 × 2 = 12 man-days for 10 sofas, so each sofa needs 1.2 man-days. Eight sofas need 9.6 man-days, and 8 men complete that in 9.6/8 = 1.2 days.
Q10. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
Answer: 120 gallons
Explanation: Setting up the equation for 15-minute fill time with both inlet pipes and waste pipe gives a waste rate of 1/40 tank per minute = 3 gallons/min, so capacity = 120 gallons.
Q11. 8 children and 12 men complete a certain piece of work in 9 days. If each child takes twice the time taken by a man to finish the work, in how many days will 12 men finish the same work?
Answer: 12 days
Explanation: Since each child takes twice a man's time, 8 children = 4 men, making a total of 16 men; 12 men will take 16×9/12 = 12 days.
Q12. 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_________?
Answer: 25 days
Explanation: Since A's rate equals B+C combined, and with C alone taking 50 days, working through the equations gives B alone taking 25 days.
Q13. A is twice as good a workman as B and takes 6 less days to complete a piece of work as
Answer: 12 days
Explanation: Since A is twice as productive as B, if B takes t days then A takes t/2 days; t − t/2 = 6 gives t = 12 days.
Q14. A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full the leak will empty it in. Pipes and Cisterns
Answer: 40 hrs
Explanation: Fill rate = 1/8 per hour; with the leak the net fill rate = 1/10 per hour, so the leak rate = 1/8 − 1/10 = 1/40, meaning it empties the cistern in 40 hours.
Q15. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
Answer: 30 min
Explanation: If total time is T, pipe B alone for T/2 fills T/80, and A+B together for T/2 fills T/48; setting T/80 + T/48 = 1 gives T = 30 minutes.
Q16. Two pipes X and Y fill a tank in 15 hrs. and 20 hrs. respectively, while a third pipe 'Z' can empty the full tank in 25 hrs. All the three pipes are opened in the beginning. After 10 hrs. Z is closed. In how much time, will the tank be full?
Answer: 12 hrs
Explanation: In 10 hours all three pipes fill 23/30 of the tank; the remaining 7/30 is filled by X and Y alone (rate 7/60 per hour) in 2 more hours, totalling 12 hours.
Q17. A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How many days would it take for A, B, and C to finish the work together?
Answer: 10 days
Explanation: The correct value is 10 days. Apply the formula or arithmetic step shown in the question and
Q18. If 3 men or 4 women can construct a wall in 43 days, then the number of days that 7 men and 5 women take to construct it is:
Answer: 12 days
Explanation: 3 men = 4 women in capacity, so 7 men + 5 women = 28/3 + 5 = 43/3 women. Total work = 4 × 43 = 172 woman-days. Days = 172 ÷ (43/3) = 12 days.
Q19. If 6 men take 9 days to complete a work, how many men can complete the work in 3 days?
Answer: 18 men
Explanation: Total work = 6 × 9 = 54 man-days. To finish in 3 days, men needed = 54/3 = 18.
Q20. A can do a piece of work in 10 days and B in 15 days. If they work for a day alternatively. A beginning the work will be completed in:
Answer: 12 days
Explanation: On day 1 A does 1/10 and day 2 B does 1/15; combined in each 2-day cycle = 1/10 + 1/15 = 1/6. Six such cycles (12 days) complete the entire work.