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SSC GD 2024 PYQ — Question 44

SSC GD Const (English) - 21 Feb 2024 - Shift 3 • Quantitative Aptitude • Q44

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S1 alone can do a work in 16 days and S2 alone can do the same work in 80 days. With help of S3, they finish the same work in 6 days. In how many days S3 alone can do the same work?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 120/11 days.

 S1's rate of work is (116) ( \frac{1}{16} )  units per day, as S1 can finish the work in 16 days.

 S2's rate of work is  (180)( \frac{1}{80} ) units per day, as S2 can finish the work in 80 days.

 S1, S2, and S3 together finish the work in 6 days, so their combined rate of work is  (16)( \frac{1}{6} )units per day.

The combined rate of S1, S2, and S3 is the sum of their individual rates:

⇒ 116+180+1x=16\frac{1}{16} + \frac{1}{80} + \frac{1}{x} = \frac{1}{6}

⇒ 116=580\frac{1}{16} = \frac{5}{80}

⇒ 580+180=680=340\frac{5}{80} + \frac{1}{80} = \frac{6}{80} = \frac{3}{40}

 ⇒340+1x=16\frac{3}{40} + \frac{1}{x} = \frac{1}{6}

⇒ 1x=16−340\frac{1}{x} = \frac{1}{6} - \frac{3}{40}

⇒ 1x=20120−9120=11120\frac{1}{x} = \frac{20}{120} - \frac{9}{120} = \frac{11}{120}

⇒ x=12011 x = \frac{120}{11}