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SSC Selection Post 2022 PYQ — Question 59

SSC Selection Post - Matriculation Level 2022 - 2 Feb 2022 - Shift 3 • Quantitative Aptitude • Q59

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The breadth of a rectangular field is 7.5 m shorter than its length. One-third of the breadth is equal to one-forth of the length of the rectangle. What is the average (in m, to the nearest integer) of its length and breadth?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 26.

B = L−7.5

1/3B = 1/4L

13(L−7.5)=14L⇒4(L−7.5)=3L⇒4L−30=3L⇒L=30⇒B=30−7.5=22.5\frac{1}{3}(L - 7.5) = \frac{1}{4}L \\[6pt] \Rightarrow 4(L - 7.5) = 3L \quad \\ \Rightarrow 4L - 30 = 3L \\ \Rightarrow L = 30 \\[6pt] \Rightarrow B = 30 - 7.5 = 22.5 \\[6pt]

Average = L+B2=30+22.52=26.25\frac{L + B}{2} = \frac{30 + 22.5}{2} = 26.25 = 26m