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SSC CHSL 2024 PYQ — Question 54

SSC CHSL - 02 July 2024 - Shift 4 • Quantitative Aptitude • Q54

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In ∆ABC the straight line parallel to the side BC meets AB and AC at the points P and Q, respectively. If AP = QC, the length of AB is 12 cm and the length of AQ is 2 cm, then the length (in cm) of CQ is:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 4.

As seen in the figure

∆ABC ~ ∆APQ ( AA similarity )

⇒ ABAC\frac{AB}{AC} = ACAQ\frac{AC}{AQ}

⇒ 12AP\frac{12}{AP} = AC2\frac{AC}{2}

Let QC = AP = x

⇒ 12x\frac{12}{x}  = 2+x2\frac{2 + x}{2}

Solving for x we get

x = -6 or 4

Neglecting  -6 since the length cannot be negative 

Hence, the length of CQ is 4 cm.