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Question 26 :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?

- \\frac{1}{4})
- \\frac{1}{5})
- \\frac{6}{19})
- \\frac{7}{33})

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Given that original ratio is 4 : 9

Let us assume Lalitha gives ‘a’ chocolates to Raju ending up in a ratio of 5 : 6

\\frac{4𝑥 + 𝑎}{9𝑥 - 𝑎}) = \\frac{5}{6})

We need to find the fraction of number of marbles given by Lalitha to the initial number of Chocolates

=> We need to find the value of \\frac{a}{9x})

\\frac{4𝑥 + 𝑎}{9𝑥 - 𝑎}) = \\frac{5}{6})
Take k = 𝑎/𝑥
\\frac{4 + k}{9 - k}) = \\frac{5}{6})
11k = 21 k = \\frac{21}{11})
We need to find the value of \\frac{a}{9x})
\\frac{a}{9x}) = \\frac{k}{9}) = \\frac{21}{9 × 11})
\\frac{a}{9x}) = ** \\frac{7}{33})**

The question is **"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?" **

Choice D is the correct answer.

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