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SSC CGL 2025 PYQ — Question 56

SSC CGL - 15 Sep 2025 - Shift 1 • Quantitative Aptitude • Q56

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In △XYZ, a line segment LM is drawn parallel to YZ, with L on XY and M on XZ. If the ratio of the area of △XLM to the area of the trapezium LMYZ is 9 : 16, what is the ratio of XL to LY?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 3 : 2.

The trapezium LMYZ is the part of △XYZ outside △XLM,

[△XYZ] = [△XLM] + [trapezium LMYZ]

Let [△XLM] = 9k, [trapezium] = 16k  

[△XYZ] = 9k + 16k = 25k

Also, LM || YZ; △XLM ∼△XYZ (by AA similarity)

⇒ (XLXY)2=area of △XLMarea of △XYZ(\frac{XL}{XY})^2 = \frac{area \ of \ △XLM}{area\ of\ △XYZ}

⇒ (XLXY)=9k25k(\frac{XL}{XY}) = \sqrt{\frac{9k}{25k}}

⇒ XLXY=35\frac{XL}{XY} = \frac{3}{5}

LY = XY - XL = 5 - 3 = 2

Required ratio = XL : LY

⇒ 3 : 2