SarkariPYQ

SSC CGL 2020 PYQ — Question 28

SSC CGL Tier II - Quant - 18 Nov 2020 • Quantitative Aptitude • Q28

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In the given figure, ABCD is a rectangle and P is a point on DC such that BC = 24 cm, DP = 10cm, and CD = 15 cm. If AP produced intersects BC produced at Q, then find the length of AQ.

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 39 cm

In the given figure one can see that,

CP || AB.

So one can say that △\triangleABQ and △\trianglePCQ are similar,

PC/AB = CQ/BQ = PQ/AQ

Let CQ = x cm.

PC/AB = CQ/BQ

5/15 = x/(24 + x)

3x = x + 24

2x = 24

x = 12.

In △\trianglePCQ

PC = 5 and CQ = 12 then hypotenuse PQ = 52+122\sqrt{5^2 + 12^2} = 13

PQ = 13

PC/AB = PQ/AQ

1/3 = 13/AQ

AQ = 39 cm.