Question:

In an examination, the score of A was 10% less than that of B, the score of B was 25% more than that of C, and the score of C was 20% less than that of D. If A scored 72, then the score of D was

Updated On: Jul 28, 2025
  • 80
  • 70
  • 90
  • 60
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The Correct Option is A

Solution and Explanation

To determine the score of D, we begin by establishing relationships between the scores using the given percentage changes:
  1. Score of A: Let's assume B's score is \( x \). A scored 10% less than B: \[ A = x - 0.10x = 0.90x \]
  2. Score of B in terms of C: B scored 25% more than C. Let C's score be \( y \): \[ B = 1.25y \]
  3. Score of C in terms of D: C's score was 20% less than D. Let D's score be \( z \): \[ C = z - 0.20z = 0.80z \]
Using A's score to find D's score:
  1. We know A scored \( 72 \): \[ 0.90x = 72 \]
  2. Solving for \( x \) (B's score): \[ x = \frac{72}{0.90} = 80 \]
  3. Since \( B = 1.25y \) and \( x = 80 \): \[ 1.25y = 80 \] \[ y = \frac{80}{1.25} = 64 \]
  4. Now, using \( C = 0.80z \) and \( y = 64 \): \[ 0.80z = 64 \] \[ z = \frac{64}{0.80} = 80 \]
Thus, the score of D was 80.
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