Question

If $\frac{(3x+5y)}{(3x–5y)}=\frac{7}{3}$ , then x : y = ____.

• A. 23:6
• B. 25:6
• C. 19:7
• D. 6:25

Answer 1

The correct option is B 25:6

We have, $\frac{(3x+5y)}{(3x–5y)}=\frac{7}{3}$
Applying componendo and dividendo

$\frac{\left[\right(3x+5y)+(3x–5y\left)\right]}{\left[\right(3x+5y)–(3x–5y\left)\right]}=\frac{(7+3)}{(7–3)}$

$\Rightarrow \frac{6x}{10y}=\frac{10}{4}$

$\Rightarrow \frac{x}{y}=\frac{(10\times 10)}{(4\times 6)}=\frac{100}{24}=\frac{25}{6}$

Hence, x:y = 25:6