CAT 2018 Slot 1 QA Question & Solution
Question
Raju and Lalitha originally had marbles in the ratio 4:9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5:6. What fraction of her original number of marbles was given by Lalitha to Raju?
Options
Solution
Let the number of marbles with Raju and Lalitha initially be $4x$ and $9x$, respectively.
Let the number of marbles that Lalitha gave to Raju be $a$.
It is given that:
$$
\frac{4x + a}{9x - a} = \frac{5}{6}
$$
Multiplying both sides by $6(9x - a)$, we get:
$$
24x + 6a = 45x - 5a
$$
Simplifying further:
$$
11a = 21x \implies \frac{a}{x} = \frac{21}{11}
$$
The fraction of Lalitha's original marbles given to Raju is:
$$
\frac{a}{9x} \quad (\text{since Lalitha had } 9x \text{ marbles initially})
$$
Substituting $a = \frac{21}{11}x$ into the fraction:
$$
\frac{a}{9x} = \frac{21}{99} = \frac{7}{33}
$$
Therefore, the correct answer is option D.