Question:

In a bag, there are some diamonds. In another bag, there are one fourth the number more than the number of diamonds in the first bag. If the difference in the number of diamonds in the first and second bag is 3, how many diamonds are there in the first bag?

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Set up the equation based on the difference between the two quantities, then solve for the unknown.
Updated On: Aug 18, 2025
  • 10
  • 16
  • 12
  • 8
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The Correct Option is C

Solution and Explanation

Let the number of diamonds in the first bag be \( x \). The number of diamonds in the second bag will be \( x + \frac{1}{4}x = \frac{5}{4}x \). According to the problem, the difference between the diamonds in the second bag and the first bag is 3. Therefore, we can set up the equation: \[ \frac{5}{4}x - x = 3 \] Simplifying the equation: \[ \frac{5}{4}x - \frac{4}{4}x = 3 \] \[ \frac{1}{4}x = 3 \] Multiplying both sides by 4: \[ x = 12 \] Thus, the number of diamonds in the first bag is \( 12 \).

Option (A) 10: Incorrect, as it does not satisfy the equation.

Option (B) 16: Incorrect, as it exceeds the correct value.

Option (D) 8: Incorrect, as it does not match the calculation.
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