If (2x − y) : (5x + 3y) = 3 : 8, t

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Target Exam

CUET

Subject

General Test

Chapter

Numerical Ability

Topic

Ratios

Question:

If (2x − y) : (5x + 3y) = 3 : 8, then (x² + y²) : (x² − y²) =

Options:

145 : 144

257 : 255

144 : 143

133 : 122

Correct Answer:

145 : 144

Explanation:

⇒ \(\frac{2x - y}{5x + 3y}\) = \(\frac{3}{8}\)

⇒ 16x - 8y = 15x + 9y

⇒ x = 17y

⇒ x : y = 17 : 1

⇒ (\( {x }^{2 } \) + \( {y }^{2 } \) ) : (\( {x }^{2 } \) - \( {y }^{2 } \) ) = (289 + 1) : (289 - 1)

⇒ 290 : 288 = 145 : 144.