Question 53

If a : b = 5 : 3, then (8a — 5b) : (8a + 5b) is equal to:

Solution

Given that,

$$a : b = 5 : 3$$

$$\dfrac{a}{b}=\dfrac{5}{3}$$

So,

$$a=5k$$ and $$b=3k$$

Now,

$$\dfrac{(8a — 5b)}{(8a + 5b)}=\dfrac{8\times 5k-5\times 3k}{8\times 5k+5\times 3k}$$

$$\Rightarrow \dfrac{(8a — 5b)}{(8a + 5b)}=\dfrac{25k}{55k}$$

$$\Rightarrow \dfrac{(8a — 5b)}{(8a + 5b)}=\dfrac{5}{11}$$

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