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