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Structure of Glucose

If a : b = ...

Question

If $a : b = 2 : 5$ , then $(3 a + 4 b) : (5 a + 6 b)$ is equal to

13 : 20

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26 : 33

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16 : 27

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18 : 35

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Solution

The correct option is B $13 : 20$
$a : b = 2 : 5 \Rightarrow \frac{a}{b} = \frac{2}{5}$
$(3 a + 4 b) : (5 a + 6 b) = \frac{3 a + 4 b}{5 a + 6 b} = \frac{\frac{3 a + 4 b}{b}}{\frac{5 a + 6 b}{b}}$
(On dividing both numerator and denominator by b)
$\frac{\frac{3 a}{b} + 4}{\frac{5 a}{b} + 6} = \frac{3 \times \frac{2}{5} + 4}{5 \times \frac{2}{5} + 6} = \frac{\frac{6}{5} + 4}{2 + 6} = \frac{26}{5} \times \frac{1}{8} = \frac{13}{20}$

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= 2 : 5

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

(3 a + 2 b) : (5 a + 3 b) = 18 : 29

a : b

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\frac{a + 2 b}{3 a + 4 b} =

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\frac{a (3 a + 4 b)}{a + 5}

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0

\frac{3 a + 5 b}{3 a - 5 b} = 5

a : b

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