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

• A. 80
• B. 70
• C. 90
• D. 60

Answer 1

The Correct Option is A

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.