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?

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7/33 — Easy Start Raju and Lalitha at $4x$ and $9x$ marbles. Lalitha gives $y$ to Raju, making the ratio $5:6$. Solve for $y$ in terms of $x$, then the required fraction is $y$ divided by Lalitha's original $9x$. 1 Set up the new ratio. Raju gains $y$, Lalitha loses $y$. $$\begin{aligned} &\frac{4x + y}{9x - y} = \frac{5}{6} \end{aligned}$$ 2 Solve for $y$. Cross-multiply and collect. $$\begin{aligned} &6(4x + y) = 5(9x - y)\ &\Rightarrow\ 24x + 6y = 45x - 5y \quad	ext{(expand)}\ &\Rightarrow\ 11y =

CAT 2018 Slot 1 — QA Question 11

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