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SSC Selection Post 2022 PYQ — Question 64

SSC Selection Post - Higher Secondary Level 2022 - 16 March 2022 - Shift 3 • Quantitative Aptitude • Q64

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A, B and C can do a work together. The ratio of the work that A and B do together with respect to what C does is 13 : 3, and the ratio of the work that B and C do together to the work that A does is 1 : 1. Which worker among the three is the most efficient?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. A.

Let the efficiencies of A, B and C be a, b and c respectively.

Given, a+bc=133\frac{a + b}{c} = \frac{13}{3}

⇒ 3a + 3b = 13c

Also, b + c = a

Putting the value of a, 3(b + c) + 3b = 13c

⇒ 6b = 10c

⇒ b = 5c3\frac{5c}{3}    ...(i)

Also, a = 5c/3 + c

⇒ a = 8c3\frac{8c}{3}    ...(ii)

Comparing the efficiencies of A, B and C,

⇒ 8c3\frac{8c}{3} > 5c3\frac{5c}{3} > c

Hence A works most efficeiently.