Question : If $p : q = 7 : 5$, then what is the value of $\frac{\left(p^2+q^2\right)}{\left(p^2-q^2\right)} ?$
Option 1: $\frac{48}{7}$
Option 2: $\frac{36}{11}$
Option 3: $\frac{37}{12}$
Option 4: $\frac{38}{5}$
Correct Answer: $\frac{37}{12}$
Solution :
Given: $p : q = 7 : 5$
Let $p = 7k$ and $q = 5k$
$\frac{\left(p^2+q^2\right)}{\left(p^2-q^2\right)}$
$=\frac{(7k)^2+(5k)^2}{(7k)^2-(5k)^2}$
$=\frac{74k^2}{24k^2}$
$=\frac{37}{12}$
Hence, the correct answer is $\frac{37}{12}$.
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