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A and B are equally efficient, and each could individually complete a piece of work in 30 days, if none took any holiday. A and B started working together on this piece of work, but A took a day off after every four days of work, while B took a day off after every five days of work. If the duo had started work on 01 August 2022, on which date was the work completed? 

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SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 3)
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  1. 19 August 2022
  2. 17 August 2022
  3. 16 August 2022
  4. 18 August 2022

Answer (Detailed Solution Below)

Option 4 : 18 August 2022
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Detailed Solution

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Given:

A and B are equally efficient, and each could individually complete a piece of work in 30 days, if none took any holiday.

A and B started working together on this piece of work, but A took a day off after every four days of work, while B took a day off after every five days of work.

Concept used:

Efficiency is inversely proportional to the time of work.

Calculation:

Lets total work in 30 units

The efficiency of A and B both is 30 /30 = 1 unit

In 1st 4 days total work 4 × 2 = 8 units

5th and 6th day 1 unit each respectively.

Total work in 6 days 8+2 = 10units

Total 10 × 3 = 30 units will be done in 6×3 = 18days

So the work will be completed in 18 August 2022

∴ The correct option is 4

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