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CAT 2018 Set-1 | Question: 87

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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?

  1. $1/4$
  2. $7/33$
  3. $1/5$
  4. $6/19$

1 Answer

1 1 vote

Given that,

The ratio of Raju and Lalitha marbles $ = 4: 9$ (originally)

  • The number of marbles Raju have $ = 4k$  
  • The number of marbles Lalitha have $ = 9k$
  • Where $k$ is some constant.

Let Lalitha gave marbles to Raju be $x.$

So$,\dfrac{4k+x}{9k-x} = \dfrac{5}{6}$

$ \Rightarrow 6(4k+x) = 5(9k-x)$

$ \Rightarrow 24k + 6x = 45k – 5x$

$ \Rightarrow 11x = 21k$

$ \Rightarrow \boxed{ x = \left( \frac{21}{11} \right) k} $

$\therefore$ The fraction of Lalitha's original number of marbles given to Raju $ = \dfrac{x}{9k}$

$\qquad = \dfrac{ \left( \frac{21}{11} \right)k} {9k}$

$ \qquad = \frac{21}{9 \times 11}$

$\qquad = \frac {7}{33}$

Correct Answer $ : \text{B}$

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