Ratio Proportion

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

Answer

Let the number of marbles with Raju and Lalitha initially be 4x and 9x.

Let the number of marbles that Lalitha gave to Raju be y.

Given that,

(4x + y)/(9x - y) = 5/6

24x + 6y = 45x – 5y

11y = 21x

y/x = 21/11

As Lalitha had 9x marbles initially, fraction of original marbles given to Raju by Lalitha = y/9x

y/9x = 21/99

= 7/33 

The correct option is B.