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Chain Rule of Differentiation

If 3p+4q:3r...

Question

If $(3 p + 4 q) : (3 r + 4 s) = (3 p - 4 q) : (3 r - 4 s),$ the value of $p s : q r$ is

A

3 : 4

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B

1 : 1

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C

4 : 3

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D

9 : 16

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Solution

The correct option is A $1 : 1$
$(3 p + 4 q) : (3 r + 4 s) = (3 p + 4 q) : (3 r + 4 s) \Rightarrow \frac{3 p + 4 q}{3 r + 4 s} = \frac{3 p - 4 q}{3 r - 4 s} \Rightarrow \frac{3 p + 4 q}{3 p - 4 q} = \frac{3 r + 4 s}{3 r - 4 s}$

$\Rightarrow \frac{3 p + 4 q + 3 p - 4 q}{3 p + 4 q - 3 p + 4 q} = \frac{3 r + 4 s + 3 r - 4 s}{3 r + 4 s - 3 r + 4 s}$ (applying componendo and dividendo)
$\Rightarrow \frac{6 p}{8 q} = \frac{6 r}{6 s} \Rightarrow p s = q r \Rightarrow \frac{p s}{q r} = 1 \Rightarrow p s : q r = 1 : 1$

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