If $\frac{(3 x + 5 y)}{(3 x - 5 y)} = \frac{7}{3}$ , find x:y.

23:6

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25:6

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19:7

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6:25

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Solution

The correct option is B
25:6

We have, $\frac{(3 x + 5 y)}{(3 x - 5 y)} = \frac{7}{3}$
Applying componendo and dividendo
$\frac{[(3 x + 5 y) + (3 x - 5 y)]}{[(3 x + 5 y) - (3 x - 5 y)]} = \frac{(7 + 3)}{(7 - 3)}$
Or, $\frac{6 x}{10 y} = \frac{10}{4}$
Or, $\frac{x}{y} = \frac{(10 \times 10)}{(4 \times 6)} = \frac{100}{24} = \frac{25}{6}$

Hence, x:y = 25:6

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