SSC CGL Preparation – Day 7

MCQs – Time and Work

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1. A can complete a work in 12 days and B in 16 days. In how many days will they complete the work together?

A) 6.86 days
B) 6.5 days
C) 7 days
D) 9 days

Answer: A
Solution:
A’s 1 day work = 1/12, B’s = 1/16
Combined 1 day = 1/12 + 1/16 = (4 + 3)/48 = 7/48
Total time = 48/7 ≈ 6.86 days

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2. A can do a work in 10 days, B is twice as efficient as A. How many days will B take to complete the same work alone?

A) 15
B) 5
C) 20
D) 10

Answer: B
Solution:
If B is twice as efficient, he’ll take half the time.
⇒ B = 10/2 = 5 days

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3. A and B can do a piece of work in 8 days. B alone can do it in 12 days. How many days will A take alone?

A) 24
B) 10
C) 18
D) 20

Answer: A
Solution:
A + B’s 1 day work = 1/8, B’s = 1/12
A’s = 1/8 – 1/12 = (3 – 2)/24 = 1/24
⇒ A alone = 24 days

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4. A can complete a work in 15 days. He worked for 5 days, and then B finished the rest in 10 days. How long would B take to complete the whole work alone?

A) 15
B) 20
C) 25
D) 30

Answer: D
Solution:
A’s 5-day work = 5/15 = 1/3
Remaining = 2/3
B does 2/3 in 10 days
⇒ Full work = 10 × 3/2 = 15 days
⇒ B alone = 15 days

Wait! That’s inconsistent—A already did 1/3, remaining 2/3 done in 10 days.
So, B’s 1-day work = (2/3)/10 = 1/15
⇒ B takes 15 days, not 30.

✔ Corrected Answer: A

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5. A, B, and C can complete a work in 20, 30, and 60 days respectively. In how many days can they complete it together?

A) 10
B) 8
C) 12
D) 15

Answer: B
Solution:
A = 1/20, B = 1/30, C = 1/60
Combined = LCM = 60
⇒ (3 + 2 + 1)/60 = 6/60 = 1/10
⇒ Total time = 10 days

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6. If A is 2 times as efficient as B, and B can finish a task in 18 days, how long will they take working together?

A) 6
B) 9
C) 12
D) 15

Answer: B
Solution:
A takes 18/2 = 9 days
Combined 1 day = 1/9 + 1/18 = (2 + 1)/18 = 3/18 = 1/6
⇒ Time = 6 days

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7. 2 men and 3 women can do a piece of work in 12 days. 3 men and 2 women can do it in 10 days. In how many days can 1 man alone do the work?

A) 18
B) 20
C) 37.5
D) 30

Answer: C
Solution:
Let 1 man’s 1-day work = M, woman = W
2M + 3W = 1/12 → (1)
3M + 2W = 1/10 → (2)

Multiply (1) by 3 → 6M + 9W = 1/4
Multiply (2) by 2 → 6M + 4W = 1/5

Subtract: (6M + 9W – 6M – 4W) = (1/4 – 1/5)
⇒ 5W = 1/20 ⇒ W = 1/100
Put in (1): 2M + 3/100 = 1/12
⇒ 2M = 1/12 – 3/100 = (25 – 9)/300 = 16/300
⇒ M = 8/300 = 2/75
So 1 man = 2/75 per day → Time = 75/2 = 37.5 days

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8. A can complete 80% of a work in 8 days. He works for 5 days, then B finishes the rest in 4 days. How long will B take to complete the full work alone?

A) 10
B) 15
C) 12
D) 8

Answer: D
Solution:
80% in 8 days ⇒ 100% in 10 days
So A’s 1-day work = 1/10
5 days → 5/10 = 0.5 or 50%
Remaining = 50% in 4 days ⇒ B = 1/8
Full work = 8 days
Wait! 50% in 4 days ⇒ B = 1/8 ⇒ Full work = 8 days

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9. A tank can be filled by Pipe A in 24 mins, and Pipe B in 32 mins. If both pipes are opened together, how long to fill 3/4th of the tank?

A) 10.3
B) 12.5
C) 14.4
D) 16

Answer: A
Solution:
A = 1/24, B = 1/32 ⇒ Combined = (4 + 3)/96 = 7/96
Time for full tank = 96/7
3/4th tank = (96/7) × 3/4 = 72/7 = 10.28 ≈ 10.3 mins

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10. A and B can do a job in 16 and 24 days respectively. They work together for 6 days, then A leaves. How many more days will B take?

A) 10
B) 12
C) 9
D) 8

Answer: C
Solution:
A = 1/16, B = 1/24
6 days work = (1/16 + 1/24) × 6 = (5/48) × 6 = 5/8
Remaining = 3/8
B alone = (3/8) / (1/24) = 3/8 × 24 = 9 days