If a $:$ b $= 2 : 5$ , then find $(3 a + 4 b) : (5 a + 6 b)$ .

\frac{11}{20}

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\frac{13}{20}

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\frac{1}{20}

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\frac{3}{20}

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Solution

The correct option is B $\frac{13}{20}$
$\frac{a}{b} = \frac{2}{5} \Rightarrow b = (5 / 2^{a}) ∴ \frac{3 a + 4 b}{5 a + 6 b} = \frac{3 a + 4 \times \frac{5}{2} b}{5 a + 6 \times \frac{5}{2} b}$
$\Rightarrow \frac{3 a + 4 b}{5 a + 6 b} = \frac{13 a}{20 a} = \frac{13}{20}$

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Similar questions

a : b = 2 : 5

(3 a + 4 b) : (5 a + 6 b)

a + b = 5

a^{2} + b^{2} = 11

a^{3} + b^{3} = 20

Find the coefficient of $x^{8} y^{12}$ in the expansion of $(x + 2 y)^{20}$

$\frac{2}{3} + \frac{- 4}{5} + \frac{7}{15} + \frac{- 11}{20} = ?$

(a) $- \frac{1}{5}$

(b) $- \frac{4}{15}$

(d) $- \frac{7}{30}$

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