If 6x + 4y/6x - 4y = 8/6 then what is the value of {x²}{y²}?

Correct Answer is : 1969196/99196

Correct Answer is : 1969196/99196

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UPSC CDS 1 2021 Math Paper

Question : 100 of 100

Marks: +1, -0

\frac{6x + 4y}{6x - 4y} = \frac{8}{6}

\frac{x^{2}}{y^{2}}

Solution:

Concept:

Use cross-multiplication to find the ratio

\frac{x}{y}

, then square it to get

\frac{x^{2}}{y^{2}}

Explanation:

Given:

\frac{6x+4y}{6x-4y} = \frac{8}{6} = \frac{4}{3}

Cross-multiply:

3(6x+4y) = 4(6x-4y)

Expand:

18x + 12y = 24x - 16y

Bring like terms:

12y + 16y = 24x - 18x

This gives

28y = 6x

\frac{x}{y} = \frac{28}{6} = \frac{14}{3}

Square both sides:

\frac{x^{2}}{y^{2}} = \left(\frac{14}{3}\right)^{2} = \frac{196}{9}

Answer:

The value of

\frac{x^{2}}{y^{2}}

\frac{196}{9}

, which corresponds to option C.

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