What is the value of \(\rm \frac{X}{Y}\) if \(\rm \frac{X-5Y}{X+5Y}=\frac{7}{13}\).

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SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 4)
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  1. \(\frac{23}{7}\)
  2. \(\frac{24}{9}\)
  3. \(\frac{50}{3}\)
  4. \(\frac{100}{7}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{50}{3}\)
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Detailed Solution

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Given:

\(\rm \frac{X-5Y}{X+5Y}=\frac{7}{13}\)

Calculation:

⇒ \(\rm \frac{X-5Y}{X+5Y}=\frac{7}{13}\)

⇒ 13 × (X - 5Y) = 7 × (X + 5Y)

⇒ 13 X - 65 Y = 7 X + 35 Y

⇒ 13 X - 7 X = 65 Y + 35 Y

⇒ 6 X = 100 Y

⇒ X/Y = 100/6 = 50/3

∴ The correct answer is 50/3.

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