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CAT 2003 Slot 2 — QA Question 35

Similarity of TrianglesEasy

In the figure (not drawn to scale) given below, P is a point on AB such that AP : PB = 4 : 3. PQ is parallel to AC and QD is parallel to CP. In ∆ARC, ∠ARC = 90°, and in ΔPQS, ∠PSQ = 90°. The length of QS is 6 cm. What is the ratio AP : PD?

Answer & solution

Correct answer: 7 : 3

  • A

    10 : 3

  • B

    2 : 1

  • 7 : 3

  • D

    8 : 3

Solution

In ∆ABC, PQ is parallel to AC,

BP : AP = BQ : QC = 3 : 4

In ∆PBC, QD is parallel to CP,

BD : DP = BQ : QC = 3 : 4

The given figure may be depicted as follows:

Let AP = 4x and PB = 3x

Since DB : PD = 3 : 4,

∴ PD = 47×3x=12x7

∴ AP : PD = 4x : 12x7 = 7 : 3.

Hence, option (c).

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CAT 2003 Slot 2 QA Q35: In the figure (not drawn to scale) given below, P is a point on AB such that AP : PB = 4 : 3. PQ is parallel t — Solution | TheCATExam