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SSC GD 2024 PYQ — Question 60

SSC GD Const (English) - 26 Feb 2024 - Shift 4 • Quantitative Aptitude • Q60

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E, F, and G together can complete a work in 20 days. E and F together can complete the same work in 50 days. G alone can finish the same work in how many days?

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 100/3 days.

 E 's rate of working be  1 / e (work per day),

 F's rate of working be 1 / f,

 G 's rate of working be 1/ g .

E, F, and G together complete the work in 20 days:

⇒ 1e+1f+1g=120\frac{1}{e} + \frac{1}{f} + \frac{1}{g} = \frac{1}{20}

E and F together complete the work in 50 days:

⇒ 1e+1f=150\frac{1}{e} + \frac{1}{f} = \frac{1}{50}

⇒ (1e+1f+1g)−(1e+1f)=120−150\left( \frac{1}{e} + \frac{1}{f} + \frac{1}{g} \right) - \left( \frac{1}{e} + \frac{1}{f} \right) = \frac{1}{20} - \frac{1}{50}

⇒ 1g=120−150\frac{1}{g} = \frac{1}{20} - \frac{1}{50}

⇒ 120−150=5100−2100=3100\frac{1}{20} - \frac{1}{50} = \frac{5}{100} - \frac{2}{100} = \frac{3}{100}

⇒ 1g=3100\frac{1}{g} = \frac{3}{100}

⇒ g = 100 / 3