Question 70

If a : b = 3 : 4, find the value of (7a - 4b) : (8a + 4b).

Solution

Given, a : b = 3 : 4

$$\Rightarrow$$ $$\frac{a}{b}=\frac{3}{4}$$

$$\Rightarrow$$ $$\frac{4a}{4b}=\frac{3}{4}$$

$$\Rightarrow$$ $$4b=\frac{16a}{3}$$

(7a - 4b) : (8a + 4b) $$=\frac{7a-4b}{8a+4b}$$

$$=\frac{7a-\frac{16a}{3}}{8a+\frac{16a}{3}}$$

$$=\frac{\frac{21a-16a}{3}}{\frac{24a+16a}{3}}$$

$$=\frac{5a}{40a}$$

$$=\frac{1}{8}$$

$$=$$ 1 : 8

Hence, the correct answer is Option A

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