SSC CGL Time and Work Verified Practice Test 9

1. 24 men can complete a task in 16 days. 32 men will complete it in:

• A. 10 days
• B. 11 days
• C. 12 days (Correct)
• D. 14 days

Explanation: 24×16=32×d → d=12 days.

2. A is 3 times as fast as B. A takes 40 days less than B. Days to complete together:

• A. 10 days
• B. 12 days
• C. 15 days (Correct)
• D. 18 days

Explanation: If B=x days, A=x/3. x−x/3=40 → 2x/3=40 → x=60. A=20 days. Together=1/20+1/60=4/60=1/15. 15 days.

3. Two pipes A and B fill a tank in 15 and 20 minutes. When both are opened with a drain pipe C, the tank fills in 12 minutes. How long does C take to empty the full tank?

• A. 24 min
• B. 30 min (Correct)
• C. 40 min
• D. 60 min

Explanation: A+B rate = 1/15 + 1/20 = 7/60. Net rate with drain = 1/12 = 5/60. Drain rate = 2/60 = 1/30, so C empties the tank in 30 minutes.

4. A can do a piece of work in 12 days, working 8 hours a day. B can do same in 15 days working 6 hours a day. How many days for both working 9 hours a day?

• A. 4 days
• B. 5 days (Correct)
• C. 6 days
• D. 7 days

Explanation: A: 96 man-hours. B: 90 man-hours. Total=186 man-hrs? No. Work by A=12×8=96 man-hrs per whole job. Work by B=15×6=90 man-hrs per whole job. So 1 man-hour=1/96 and 1/90 of job? No: same job in different man-hours doesn't work. A's work-rate=1/(12×8)=1/96 job/hour. B's=1/(15×6)=1/90. Together=1/96+1/90=(90+96)/(96×90)=186/8640=31/1440. Days at 9h/day=1/(31/1440×9)=1440/279≈5.16≈5 days.

5. A works for 5 days, B for 8 days, and C for 10 days to complete a task. If A, B, C can individually do it in 20, 40, and 80 days respectively, how much work remains?

• A. 0
• B. 1/4
• C. 1/8
• D. None (Correct)

Explanation: A:5/20=1/4, B:8/40=1/5, C:10/80=1/8. Total done=10/40+8/40+5/40=23/40. Remaining=17/40, which matches none of the listed options.

6. If 10 men or 20 women can complete a job in 14 days, 5 men and 10 women will take:

• A. 14 days (Correct)
• B. 16 days
• C. 18 days
• D. 20 days

Explanation: 1 man = 2 women. 5 men+10 women = 10+10=20 women. Same as 20 women → 14 days.

7. Pipe A fills a tank in 20 hours. After 5 hours, pipe B also opens and the tank fills in 10 more hours. B alone fills the tank in:

• A. 20 hours
• B. 30 hours
• C. 40 hours (Correct)
• D. 50 hours

Explanation: A fills 5/20 = 1/4 in 5 hours. Remaining 3/4 is filled by A+B in 10 hours, so A+B rate = 3/40. Since A rate is 1/20 = 2/40, B rate is 1/40.

8. Three men A, B, C earn total ₹1080 in 9 days. A earns 3/4 of B, B earns 4/5 of C per day. C earns:

• A. ₹40
• B. ₹44
• C. ₹48
• D. ₹50 (Correct)

Explanation: Let C=c per day. B=4c/5. A=3/4×4c/5=3c/5. Total per day=(3c/5+4c/5+c)=12c/5. 9×12c/5=1080 → c=1080×5/(9×12)=50. C per day=₹50.

9. P alone can do a job in 12 days and Q alone in 16 days. They work alternately, starting with P. The job is completed in:

• A. 13 days
• B. 13 1/3 days (Correct)
• C. 13 1/2 days
• D. 14 days

Explanation: In 12 days, six P-Q cycles complete 6 x (1/12 + 1/16) = 42/48 = 7/8 of the work. On day 13, P completes 1/12 more, leaving 1/24. Q takes (1/24)/(1/16) = 2/3 day, so total time is 13 1/3 days.

10. Three pipes fill a tank in 6, 8, and 12 hours. All open together, tank fills in:

• A. 2.18 hours
• B. 2.67 hours (Correct)
• C. 3 hours
• D. 3.5 hours

Explanation: 1/6+1/8+1/12=4/24+3/24+2/24=9/24=3/8. Time=8/3≈2.67 hours.

11. A can do a work in 15 days and B in 20 days. They start together but A leaves 5 days before completion. Total days:

• A. 10
• B. 11 (Correct)
• C. 12
• D. 13

Explanation: Let total days=d. Both work (d−5) days, then B alone 5 days. (d−5)/15+(d−5)/20+5/20=1. (d−5)(7/60)+1/4=1. (d−5)×7/60=3/4. d−5=45/7≈6.4. d≈11.4. Approx 11.

12. 12 persons complete 60% of a work in 15 days. Extra persons needed to complete the rest in 8 days are:

• A. 3 (Correct)
• B. 4
• C. 5
• D. 6

Explanation: 60% work needs 12 x 15 = 180 man-days, so full work needs 300 man-days. Remaining 40% needs 120 man-days. In 8 days, 15 persons are needed, so extra persons = 15 - 12 = 3.

13. A and B together earn ₹560 in 7 days. A earns ₹40/day and B earns ₹x/day. Find x.

• A. ₹30
• B. ₹35
• C. ₹40 (Correct)
• D. ₹45

Explanation: Total/day=560/7=80. B=80−40=₹40/day.

14. A completes work in 8 days and B in 16 days. Together they finish in:

• A. 7 days
• B. 8 days
• C. 6 days
• D. 5 days (Correct)

Explanation: Combined rate = 1/A + 1/B.

15. A completes work in 9 days and B in 18 days. Together they finish in:

• A. 7 days
• B. 8 days
• C. 6 days (Correct)
• D. 9 days

Explanation: Combined rate = 1/A + 1/B.