Aarif, Arun and Abraham can do a work in 12, 20 and 24 days, respectively. They all begin together. Arun leaves the work 3 days and Abraham 6 days before its completion. In how many days is the work finished?

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SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 4)
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  1. 8
  2. 10
  3. 11
  4. 9

Answer (Detailed Solution Below)

Option 1 : 8
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Detailed Solution

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Given:

Aarif, Arun and Abraham can do a work in 12, 20 and 24 days, respectively.

They all begin together. Arun leaves the work 3 days and Abraham 6 days before its completion.

Concept used:

Total work = Efficiency × Time

Calculation:

Let the total time taken by them be x days

Now,

LCM of 12, 20, and 24 = 120 i.e total work

So, efficiency of Aarif = 120/12

⇒ 10

Efficiency of Arun = 120/20

⇒ 6

Efficiency of Abraham = 120/24

⇒ 5

According to the question,

x × 10 + (x - 3) × 6 + (x - 6) × 5 = 120

⇒ 10x + 6x - 18 + 5x - 30 = 120

⇒ 21x = 120 + 48

⇒ 21x = 168

⇒ x = 8

∴ The required time is 8 days.

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