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

3:2

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4:3

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1:1

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5:3

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Solution

The correct option is B
4:3

$\frac{3 a + 2 b}{5 a + 3 b} = \frac{18}{29} \Rightarrow \frac{b [3 (\frac{a}{b}) + 2]}{b [5 (\frac{a}{b}) + 3]} = \frac{18}{29}$
Let $\frac{a}{b} = x$
Then, $29 (3 x + 2) = 18 (5 x + 3) \Rightarrow 87 x + 58 = 90 x + 54 \Rightarrow 87 x - 90 x = - 58 + 54 \Rightarrow - 3 x = - 4 \Rightarrow x = \frac{4}{3} ∴ \frac{a}{b} = \frac{4}{3} \Rightarrow a : b = 4 : 3$

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\frac{a - b}{a + b} + \frac{3 a - 2 b}{a + b} + \frac{5 a - 3 b}{a + b} + \dots t o 11 t e r m s

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

a : b

(3 a + 2 b) ∶ (5 a + 3 b) = 18 ∶ 29

a : b

(3 a + 2 b) - (- 2 a - 5 b)

\frac{a - b}{a + b} + \frac{3 a - 2 b}{a + b} + \frac{5 a - 3 b}{a + b} . . . .

11

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