CAT 2018 Slot 1 QA Question 3: 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.

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.

Accepted Answer

Let Raju and Lalitha originally have $4k$ and $9k$ marbles respectively.
Let Lalitha give $x$ marbles to Raju.
$\dfrac{4k + x}{9k - x} = \dfrac{5}{6}$
$24k + 6x = 45k - 5x$
$11x = 21k$
$x = \dfrac{21k}{11}$
Required fraction of Lalitha’s original marbles is
$\dfrac{\dfrac{21k}{11}}{9k} = \dfrac{21}{

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?