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Laws of Exponents

Mark the corr...

Question

Mark the correct alternative in the following question:

$If a : b = 2 : 5, then \frac{3 a + 2 b}{4 a + b} = (a) \frac{16}{13} (b) \frac{13}{16} (c) \frac{25}{22} (d) \frac{20}{21}$

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Solution

$As, a : b = 2 : 5 \Rightarrow \frac{a}{b} = \frac{2}{5} Let a = 2 x and b = 5 x . Then, \frac{3 a + 2 b}{4 a + b} = \frac{3 \times 2 x + 2 \times 5 x}{4 \times 2 x + 5 x} = \frac{6 x + 10 x}{8 x + 5 x} = \frac{16 x}{13 x} = \frac{16}{13}$

Hence, the correct alternative is option (a).

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