A and B can complete a piece of work in 12 days and 18 days, respectively. If they work at it alternatively, A beginning, in how many days will the work be finished?

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SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 2)
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  1. \(14\frac{2}{3}\)
  2. \(14\frac{1}{3}\)
  3. \(15\frac{1}{3}\)
  4. \(15\frac{2}{3}\)

Answer (Detailed Solution Below)

Option 2 : \(14\frac{1}{3}\)
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Detailed Solution

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Given:- 

A  alone can do a piece of work in 12 days. 

B alone can complete it in 18 days

Formula used:-

Total work = efficiency ×  time taken 

Calculation:- 
 
  Time  Efficiency Total work
A 12 3 36
B 18 2

So,

Total work in 2 days = 3 + 2 = 5 unit 

Total work in 14 days = 5 ×
 7 = 35 unit

Remaining work = 36 -35 = 1 unit

As per the question,

Now remaining the work from by the "A" = 1/3

Total days = 14 + 1/3 = \(14\frac{1}{3} \)

∴ The required answer is \(14\frac{1}{3}\).
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