Manish, Nakul and Pintoo alone can complete a certain work in 21days, 28 days and 15 days, respectively. Manish and Pintoo started the work together while Nakul joined them after 5 days and worked with them till the completion of the work. For how many days did Nakul work?

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SSC CPO 2024 Official Paper-I (Held On: 28 Jun, 2024 Shift 2)
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  1. 5\(\frac{1}{2}\)
  2. 2\(\frac{6}{7}\)
  3. 2\(\frac{1}{2}\)
  4. 3\(\frac{1}{2}\)

Answer (Detailed Solution Below)

Option 2 : 2\(\frac{6}{7}\)
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SSC CPO : General Intelligence & Reasoning Sectional Test 1
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Detailed Solution

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Given:

Manish alone can complete the work in 21 days.

Nakul alone can complete the work in 28 days.

Pintoo alone can complete the work in 15 days.

Manish and Pintoo started the work together.

Nakul joined them after 5 days.

Formula Used:

Work done by a person in 1 day = 1 / Total days taken by the person to complete the work

Total work = Sum of work done by all in the given days

Calculation:

Work done by Manish in 1 day = 1 / 21

Work done by Pintoo in 1 day = 1 / 15

Work done by Nakul in 1 day = 1 / 28

Work done by Manish and Pintoo together in 1 day = (1 / 21) + (1 / 15)

⇒ Work done by Manish and Pintoo together in 1 day = (15 + 21) / 315

⇒ Work done by Manish and Pintoo together in 1 day = 36 / 315 = 12 / 105 = 4 / 35

Work done by Manish and Pintoo in 5 days = 5 × (4 / 35)

⇒ Work done by Manish and Pintoo in 5 days = 20 / 35 = 4 / 7

Remaining work = 1 - 4 / 7

⇒ Remaining work = 3 / 7

Work done by Manish, Pintoo, and Nakul together in 1 day = (1 / 21) + (1 / 15) + (1 / 28)

⇒ Work done by Manish, Pintoo, and Nakul together in 1 day = (20 + 28 + 15) / 420

⇒ Work done by Manish, Pintoo, and Nakul together in 1 day = 63 / 420 = 3 / 20

Let Nakul worked for x days after joining:

Total work done in x days = x × (3 / 20)

Remaining work = 3 / 7

⇒ x × (3 / 20) = 3 / 7

⇒ x = (3 / 7) × (20 / 3)

⇒ x = 20 / 7

⇒ x = 2\(\frac{6}{7}\) days

Nakul worked for 2\(\frac{6}{7}\) days.

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