In a test, B scored 54 marks and A scored 75 marks. A’s marks were…

Concept

To express one quantity as a percentage of another, divide the quantity being compared by the reference quantity and multiply the ratio by 100.

The denominator must be the quantity named after the word ‘of’; therefore, ‘A as a percentage of B’ uses B’s marks as the denominator.

Application

1. Let A’s marks be 75 and B’s marks be 54.

2. Required percentage = (A’s marks ÷ B’s marks) × 100.

3. Required percentage = (75 ÷ 54) × 100 = (25 ÷ 18) × 100.

4. Required percentage = 138.888…%, which rounds to 138.89%.

Cross-check

Since 75 is greater than 54, A’s marks must be more than 100% of B’s marks; 138.89% satisfies this magnitude check.

Therefore, A’s marks were approximately 138.89% of B’s marks.