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?
- 1/4
- 7/33
- 1/5
- 6/19
The Correct Option is B
Solution and Explanation
Let the original number of marbles with Raju and Lalitha be 4x and 9x respectively. After Lalitha gives away some marbles to Raju, let the number of marbles given be y.
After the transfer, the marbles count changes to:
- Raju: 4x + y
- Lalitha: 9x - y
According to the new ratio:
(4x + y)/(9x - y) = 5/6
Cross-multiplying gives:
6(4x + y) = 5(9x - y)
Expanding both sides:
24x + 6y = 45x - 5y
Simplifying gives:
24x + 6y + 5y = 45x
24x + 11y = 45x
11y = 45x - 24x
11y = 21x
Solve for y:
y = 21x/11
We need the fraction of the original number of marbles given away by Lalitha, which is y/9x:
(21x/11) / (9x) = 21/99 = 7/33
Therefore, Lalitha gave 7/33 of her original number of marbles to Raju.
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