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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?

1. \\frac{1}{4})
2. \\frac{1}{5})
3. \\frac{6}{19})
4. \\frac{7}{33})

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Ratio and Proportion

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?"

Hence, the answer is \\frac{7}{33})

Choice D is the correct answer.