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Abhay and Bharat can complete a certain piece of work in 9 and 11 days, respectively, They started to work together, and after 3 days, Bharat left. In how many days will Abhay complete the remaining work?

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RPF Constable 2024 Official Paper (Held On: 02 Mar, 2025 Shift 1)
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  1. \(\frac{117}{33} \)
  2. \(\frac{117}{35} \)
  3. \( \frac{115}{33} \)
  4. \(\frac{116}{34}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{117}{33} \)
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Detailed Solution

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Given:

Abhay's time to complete work (A) = 9 days

Bharat's time to complete work (B) = 11 days

They work together for 3 days.

Formula used:

Remaining work = Total work - (Work done together in 3 days)

Time taken by A to complete remaining work = Remaining work / (Work done by A in 1 day)

Calculations:

Work done by Abhay in 1 day = 1/9

Work done by Bharat in 1 day = 1/11

Work done together in 1 day = 1/9 + 1/11

⇒ Work done together in 1 day = (11 + 9) / (9 × 11) = 20 / 99

Work done together in 3 days = 3 × (20 / 99) = 20 / 33

Remaining work = 1 - 20/33 = 13/33

Time taken by Abhay to complete remaining work = (13/33) / (1/9)

⇒ Time taken by Abhay to complete remaining work = 117 / 33

∴ The correct answer is option 1.

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