Multiple choice

One hundred diamonds, each worth Rs. 25,000, are to be divided into two groups, such that one-fourth of the number of diamonds in the first group would be 20 more than one-sixth of the number of diamonds in the second group. What is the ratio of the number of diamonds in the first group to that in the second group?

  1. 22 : 3

  2. 3 : 22

  3. 21 : 5

  4. 7 : 3
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A Correct answer
AI explanation

Let the number of diamonds in the first group be x, making the number in the second group 100 minus x. The problem states that x divided by 4 equals the quantity 100 minus x divided by 6 plus 20. Multiplying the entire equation by 12 to clear fractions results in 3x equals 200 minus 2x plus 240, which simplifies to 5x equals 440, so x equals 88. The second group has 100 minus 88, which is 12 diamonds, making the ratio of the first group to the second group 88 divided by 12, which simplifies to 22 : 3.

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