Topic-wise Time & Work MCQs for CDAC C-CAT preparation with answers and explanations.
Q1.
A can do a work in 10 days and B can do it in 15 days. In how many days can they do it together?
A5 days
B8 days
C6 days
D12 days
Show Answer & Explanation
Correct Answer: C - 6 days
Combined rate = 1/10 + 1/15 = 1/6. So time = 6 days.
Q2.
If 6 men can complete a work in 8 days, how many days will 4 men take?
A12 days
B10 days
C14 days
D16 days
Show Answer & Explanation
Correct Answer: A - 12 days
Work = 6×8 = 48 man-days. For 4 men: 48/4 = 12 days.
Q3.
A can do a work in 12 days. B is 50% more efficient than A. In how many days can B complete the work?
A6 days
B8 days
C9 days
D10 days
Show Answer & Explanation
Correct Answer: B - 8 days
B is 1.5 times efficient. B's time = 12/1.5 = 8 days.
Q4.
A does 40% of a work in 8 days. He then calls B and they complete the remaining work in 6 days. In how many days can B alone do the work?
A35 days
B30 days
C20 days
D40 days
Show Answer & Explanation
Correct Answer: C - 20 days
A completes 40% in 8 days, so A works at 5% per day. During the next 6 days, A completes 30% and B completes the remaining 30%. B also works at 5% per day, so B alone needs 20 days.
Q5.
A and B can do a work in 8 days. B and C can do it in 12 days. A and C can do it in 8 days. In how many days can A alone do the work?
A16 days
B12 days
C20 days
D24 days
Show Answer & Explanation
Correct Answer: B - 12 days
2(A+B+C) = 1/8+1/12+1/8 = 1/3. A+B+C = 1/6. A = 1/6-1/12 = 1/12. A = 12 days.
Q6.
A can complete a job in 20 days. A and B together complete it in 12 days. In how many days can B alone complete it?
12 men can complete a work in 18 days. 6 days after they started, 4 more men joined. In how many more days will the work be completed?
A9 days
B8 days
C10 days
D12 days
Show Answer & Explanation
Correct Answer: A - 9 days
Total work = 12×18 = 216. Done in 6 days = 72. Remaining = 144. 16 men: 144/16 = 9 days.
Q8.
If 5 men or 8 women can do a work in 12 days, in how many days can 2 men and 3 women do it?
A15 days
B12 days
C18 days
D20 days
Show Answer & Explanation
Correct Answer: A - 15 days
5M = 8W, so 1M = 8/5 W. 2M+3W = 16/5+3 = 31/5 W. Time = (8×12)/(31/5) = 480/31 approx 15 days.
Q9.
A tap can fill a tank in 6 hours. After half the tank is filled, 3 more similar taps are opened. What is the total time to fill the tank?
A3 hrs 30 min
B4 hours
C3 hrs 45 min
D4 hrs 30 min
Show Answer & Explanation
Correct Answer: C - 3 hrs 45 min
Half tank in 3 hrs. Remaining half with 4 taps: (1/2)÷(4/6) = 3/4 hr = 45 min. Total = 3:45.
Q10.
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 will B alone take?
A8 hours
B10 hours
C14 hours
D12 hours
Show Answer & Explanation
Correct Answer: D - 12 hours
A=1/4, B+C=1/3, A+C=1/2. C=1/2-1/4=1/4. B=1/3-1/4=1/12. B alone = 12 hours.
Q11.
A does a work in 10 days. B does it in 15 days. If they work on alternate days starting with A, in how many days will work be completed?
A11 days
B14 days
C13 days
D12 days
Show Answer & Explanation
Correct Answer: D - 12 days
In 2 days: 1/10+1/15 = 1/6. In 10 days: 5/6 done. Day 11: A does 1/10. Total = 5/6+1/10 = 14/15. Day 12: B finishes. Total = 12 days.
Q12.
Two pipes can fill a tank in 15 and 20 minutes. An outlet pipe can empty it in 30 minutes. With all three open, how long to fill?
A10 min
B12 min
C15 min
D18 min
Show Answer & Explanation
Correct Answer: B - 12 min
Net rate = 1/15 + 1/20 - 1/30 = (4+3-2)/60 = 5/60 = 1/12. Time = 12 min.
Q13.
A can complete work in 12 days working 8 hours a day. B can complete in 8 days working 10 hours a day. In how many days can they together complete working 8 hours a day?
A4 days
B5 days
C5.5 days
D6 days
Show Answer & Explanation
Correct Answer: C - 5.5 days
A requires 12*8 = 96 man-hours, and B requires 8*10 = 80 man-hours. Working together for 8 hours per day, their daily work is 8/96 + 8/80 = 1/12 + 1/10 = 11/60. Time required is 60/11, about 5.5 days.
Q14.
A alone can do 1/4 of the work in 2 days. B alone can do 1/3 of the work in 3 days. How many days for both together to complete?
A6 days
B5 days
C72/17 days
D8 days
Show Answer & Explanation
Correct Answer: C - 72/17 days
A completes the work in 8 days and B completes it in 9 days. Together their rate is 1/8 + 1/9 = 17/72, so the required time is 72/17 days.
Q15.
A can build a wall in 30 days. B can demolish it in 60 days. If A starts building and B joins after 15 days, when is wall complete?
A30 days
B45 days
C50 days
D60 days
Show Answer & Explanation
Correct Answer: B - 45 days
In 15 days, A builds 1/2. After that, A-B = 1/30-1/60 = 1/60 per day. Remaining 1/2 takes 30 days. Total = 45 days.
Q16.
10 men can complete work in 7 days. But 10 men start and 3 men leave after 2 days. In how many more days will work be completed?
A50/7 days
B7 days
C6 days
D9 days
Show Answer & Explanation
Correct Answer: A - 50/7 days
Total work is 10*7 = 70 man-days. The first 2 days complete 20 man-days, leaving 50 man-days. With 7 men remaining, the time required is 50/7 days.
Q17.
Wages for 45 women for 60 days are ₹81000. How many men must work 16 days to earn ₹13600 if daily wage ratio is 3:2?
A20
B35
C30
D25
Show Answer & Explanation
Correct Answer: D - 25
Woman wage/day = 81000/(45×60) = 30. Man wage/day = 45. Men needed: 13600/(45×16) = 18.89 ≈ 25.
Q18.
A work twice as fast as B. If B alone takes 30 days, in how many days can A and B together complete?
A8 days
B10 days
C12 days
D15 days
Show Answer & Explanation
Correct Answer: B - 10 days
A takes 15 days. Together: 1/15+1/30 = 3/30 = 1/10. Time = 10 days.
Q19.
A cistern has two pipes. One can fill it in 8 hours, other in 4 hours. With cistern full, both opened along with waste pipe. It empties in 20 hours. Waste pipe can empty in:
A2 hrs
B2.5 hrs
C3 hrs
D4 hrs
Show Answer & Explanation
Correct Answer: B - 2.5 hrs
Fill rate = 1/8+1/4 = 3/8. Net empty = -1/20. Waste = 3/8+1/20 = 17/40. Time = 40/17 ≈ 2.35 hrs ≈ 2.5 hrs.
Q20.
A is thrice as efficient as B. A takes 40 days less than B to do a job. In how many days can they together complete?
A12 days
B18 days
C15 days
D20 days
Show Answer & Explanation
Correct Answer: C - 15 days
Let B take 3x days, A takes x days. 3x-x=40, x=20. A=20, B=60. Together: 1/20+1/60=4/60=1/15. Time=15 days.
Q21.
A can do a piece of work in 12 days and B in 18 days. Together they finish it in:
If 5 machines produce 100 units in 4 hours, 8 machines produce 200 units in:
A5 hours
B4 hours
C6 hours
D8 hours
Show Answer & Explanation
Correct Answer: A - 5 hours
Rate per machine = 100/(5×4) = 5 units/hour. 8 machines = 40 units/hour. Time = 200/40 = 5 hours.
Q32.
A can complete 1/3 of work in 5 days. B can complete 2/5 of work in 10 days. Together they finish in:
A75/8 days
B10 days
C75/7 days
D12 days
Show Answer & Explanation
Correct Answer: A - 75/8 days
A completes the work in 15 days and B in 25 days. Together their rate is 1/15 + 1/25 = 8/75, so time = 75/8 days.
Q33.
A does a job in 18 days, B in 12 days. A starts alone and after 6 days B joins. Total time to complete:
A54/5 days
B12 days
C14 days
D11 days
Show Answer & Explanation
Correct Answer: A - 54/5 days
A does 6/18 = 1/3 of the job in 6 days. Remaining work is 2/3. Together A and B work at 1/18+1/12=5/36 per day, so remaining time is 24/5 days. Total time = 54/5 days.
Q34.
A pipe fills a cistern in 10 minutes. Another pipe can fill it in 15 minutes. Both opened together, cistern fills in: