CTET 2 Math and Science 07 Jul 2024 Paper

Arun is three years older than Varun
Eight years ago $\frac{5}{6}$ th of Arun's age exceeded $\frac{3}{5}$ th of Varun's age by 6 years.
The present age of Varun $\mathit{x}$ years
Calculation:
Since Arun is 3 years older than Varun:
The present age of Arun $\mathit{x}+3$
Eight years ago:
Arun's age was $\left(\mathit{x}+3\right)-8=\mathit{x}-5$ years
Varun's age was $\mathit{x}-8$ years
According to the problem, Eight years ago $\frac{5}{6}$ th of Arun's age exceeded $\frac{3}{5}$ th of Varun's age by 6 years.
$\Rightarrow \frac{5}{6}\times \left(\mathit{x}-5\right)-\frac{3}{5}\times \left(\mathit{x}-8\right)=6$
This matches the third option.
$\therefore$ The correct answer is Option (3): $\frac{5}{6}\times \left(\mathit{x}-5\right)-\frac{3}{5}\times \left(\mathit{x}-8\right)=6$