Discussion
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. If the present age of Varun is x years, then the value of x can be determined by solving the equation :
Answer: A
The equation is \(\frac{5}{6}(x - 5) - \frac{3}{5}(x - 8) = 6\).
Varun is x years old now, so Arun is x + 3. Eight years ago their ages were:
\[ \begin{aligned} \text{Arun} &= (x + 3) - 8 = x - 5 \\ \text{Varun} &= x - 8 \end{aligned} \]
Five-sixths of Arun's age then exceeded three-fifths of Varun's by 6, which is the first equation. The second swaps the two past ages, the third and fourth attach the fractions to the wrong person and use the wrong ages.
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