Marble Sharing Ratio

CAT 2019 Slot 1 · QA · Easy · Ratio & Proportion

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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. A.

    14\frac{1}{4}

  2. B.

    15\frac{1}{5}

  3. C.

    619\frac{6}{19}

  4. D.

    733\frac{7}{33}

Answer

D

Explanation

Original ratio = 4 : 9 ⇒\Rightarrow Total = 13 parts. New ratio = 5 : 6 ⇒\Rightarrow Total = 11 parts. Since total number of marbles is constant, scale ratios to make totals equal (LCM = 143): Original: Raju = 4×11=444 \times 11 = 44, Lalitha = 9×11=999 \times 11 = 99. New: Raju = 5×13=655 \times 13 = 65, Lalitha = 6×13=786 \times 13 = 78. Marbles given by Lalitha = 99−78=2199 - 78 = 21. Fraction given = 21/99=7/3321 / 99 = 7 / 33.

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