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SSC GD 2024 PYQ — Question 54

SSC GD Const (English) - 22 Feb 2024 - Shift 3 • Quantitative Aptitude • Q54

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Dinesh alone can do a work in 96 hours. Dinesh and Rahul together can do the same work in 48 hours. Rahul and Tarun together can do the same work in 16 hours. In how many hours can Tarun alone do the same work?

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 19.2 hours. 

The work rate of Dinesh = (1 / 96) of the work per hour.

The work rate of Rahul = (1 / r).

The work rate of Tarun =  (1 / t).

Dinesh and Rahul together can complete the work in 48 hours, so their combined rate is (1/ 48) of the work per hour.

⇒196+1r=148 \frac{1}{96} + \frac{1}{r} = \frac{1}{48}

 Rahul and Tarun together can complete the work in 16 hours, so their combined rate is (1 / 16) of the work per hour. 

⇒ 1r+1t=116\frac{1}{r} + \frac{1}{t} = \frac{1}{16}

⇒ 196+1r=148\frac{1}{96} + \frac{1}{r} = \frac{1}{48}

⇒ 1r=148−196\frac{1}{r} = \frac{1}{48} - \frac{1}{96}

⇒ 148=296,196=196\frac{1}{48} = \frac{2}{96}, \quad \frac{1}{96} = \frac{1}{96}

⇒ 1r=296−196=196\frac{1}{r} = \frac{2}{96} - \frac{1}{96} = \frac{1}{96}

( r = 96)

⇒ 196+1t=116\frac{1}{96} + \frac{1}{t} = \frac{1}{16}

⇒ 1t=116−196\frac{1}{t} = \frac{1}{16} - \frac{1}{96}

⇒ 116=696,196=196\frac{1}{16} = \frac{6}{96}, \quad \frac{1}{96} = \frac{1}{96}

⇒1t=696−196=596\frac{1}{t} = \frac{6}{96} - \frac{1}{96} = \frac{5}{96}

Thus, ( t = 96 / 5 = 19.2 )

Tarun can complete the work in 19.2 hours.