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SSC CPO 2024 PYQ — Question 106

SSC CPO 2024 - 27th June 2024 - Shift 1 • Quantitative Aptitude • Q106

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In ∆ABC, P is a point on AB such that PB : AP = 3 : 4 and PQ is parallel to AC. If AR and QS are perpendicular to PC and QS = 9 cm, what is the length (in cm) of AR?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 21.

As seen in the figure

In △ARC and △QSP

∠ARC = ∠PSQ = 90°

∠CAP = ∠QPB (Since PQ and AC are parallel)

Hence, △ARC ~ △QSP (AA criterion)

⇒ ARQS\frac{AR}{QS} = ACPQ\frac{AC}{PQ}

Now since △BPQ ~ △BAC,

⇒ ACPQ\frac{AC}{PQ} = 73\frac{7}{3}

Hence, AR9\frac{AR}{9} = 73\frac{7}{3}

Hence AR = 21 cm.