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CAT Previous Year Paper | CAT Ratio and Proportion Questions | Question 26

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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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Explanatory Answer

Method of solving this CAT Question from Ratio and Proportion
Ratio and Proportion - Finding the number of marbles

Given that original ratio is 4 : 9
Let us assume Lalitha gives โ€˜aโ€™ chocolates to Raju ending up in a ratio of 5 : 6
\\frac{4๐‘ฅ + ๐‘Ž}{9๐‘ฅ - ๐‘Ž}) = \\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{4๐‘ฅ + ๐‘Ž}{9๐‘ฅ - ๐‘Ž}) = \\frac{5}{6}) Take k = ๐‘Ž/๐‘ฅ \\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 ร— 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.

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