SSC CGL Preparation – Day 19

MCQs – Time and Work

---

1. A can do a piece of work in 20 days, and B can do the same work in 30 days. In how many days can they complete it together?

A) 12 days
B) 15 days
C) 18 days
D) 10 days

Answer: ✅ B
Solution:
1-day work of A = 1/20
1-day work of B = 1/30
Combined 1-day work = $$\frac{1}{20} + \frac{1}{30} = \frac{5 + 3}{60} = \frac{8}{60} = \frac{2}{15}$$
Total time = $$\frac{15}{2} = 7.5$$ days

🛑 None of the given options match. Likely intended correct answer: 7.5 days

---

2. A is 50% more efficient than B. If B can complete the work in 18 days, in how many days can A and B together finish it?

A) 7.2 days
B) 8 days
C) 10.8 days
D) 12 days

Answer: ✅ A
Solution:
Efficiency ratio A:B = 3:2
Time ratio B:A = 3:2 ⇒ A takes $$\frac{2}{3} \times 18 = 12$$ days
1-day work of A = 1/12, B = 1/18
Combined = $$\frac{1}{12} + \frac{1}{18} = \frac{5}{36}$$
Total time = $$\frac{36}{5} = 7.2$$ days

---

3. A and B together can do a work in 12 days. B alone can do it in 20 days. In how many days can A alone do it?

A) 25
B) 30
C) 15
D) 18

Answer: ✅ B
Solution:
1-day work of A+B = 1/12
1-day work of B = 1/20
1-day work of A = 1/12 − 1/20 = (5−3)/60 = 2/60 = 1/30
⇒ A takes 30 days

---

4. A and B can complete a piece of work in 16 days and 24 days respectively. They start together but A leaves after 4 days. How many more days will B take to finish the remaining work?

A) 10
B) 12
C) 14
D) 15

Answer: ✅ A
Solution:
LCM of 16 and 24 = 48 units (assumed total work)
A’s 1-day work = 3, B’s = 2
Work done in 4 days = (3+2)×4 = 20 units
Remaining = 48−20 = 28 units
B alone → 28 ÷ 2 = 14 days

🛑 Correct answer should be 14, not 10 — mismatch indicates a typo in option.
✅ Answer: 14 days

---

5. A pipe can fill a tank in 12 hours, and another pipe can empty it in 18 hours. If both pipes are opened together, how long will it take to fill the tank?

A) 36 hours
B) 24 hours
C) 54 hours
D) 72 hours

Answer: ✅ C
Solution:
1-hour fill = 1/12
1-hour empty = -1/18
Net = $$\frac{1}{12} – \frac{1}{18} = \frac{3 – 2}{36} = \frac{1}{36}$$
Time = 36 hours

---

6. A and B can do a job in 10 and 15 days respectively. They work together for 5 days, then A leaves. In how many more days will B finish the work?

A) 2
B) 3
C) 4
D) 5

Answer: ✅ B
Solution:
LCM = 30 units
A = 3/day, B = 2/day
Work in 5 days = (3+2)×5 = 25 units
Remaining = 30−25 = 5 units
B alone = 5 ÷ 2 = 2.5 days ⇒ ✅ Option not listed correctly
Correct answer: 2.5 days

---

7. If 8 men can complete a work in 24 days, how many men are required to complete the same work in 16 days?

A) 10
B) 12
C) 14
D) 15

Answer: ✅ B
Solution:
Men × Days = Constant
8 × 24 = x × 16 → x = 12 men

---

8. A tank is filled by a pipe in 20 minutes and emptied by a second pipe in 30 minutes. If both are opened together, in how much time will the tank be filled?

A) 60 min
B) 90 min
C) 120 min
D) 40 min

Answer: ✅ D
Solution:
1-min work = $$\frac{1}{20} – \frac{1}{30} = \frac{3 – 2}{60} = \frac{1}{60}$$
Time = 60 min

---

9. A can complete a work in 10 days, B in 12. If they work on alternate days starting with A, in how many days will the work be completed?

A) 10
B) 11
C) 11.5
D) 12

Answer: ✅ C
Solution:
Let total work = LCM(10,12) = 60 units
A = 6/day, B = 5/day
2-day work = 6+5 = 11 units
60 ÷ 11 = 5 full pairs = 10 days → 55 units done
Remaining = 5 units → A works next = needs 5 ÷ 6 = 0.833 days
Total = 10 + 0.83 = 10.83 ≈ 10.8 or 11 days

---

10. A is 60% as efficient as B. If B can complete a task in 20 days, in how many days can A and B together complete the task?

A) 7.5
B) 12.5
C) 8
D) 9

Answer: ✅ B
Solution:
Efficiency ratio A:B = 60:100 = 3:5
Work = LCM(20) = 100 units
B = 5/day ⇒ 20 days
A = 3/day
Together = 8/day ⇒ 100 ÷ 8 = 12.5 days