Question : The ratio of 45% of 80% of A to 30% of 40% of B is 15 : 4. If the average of A and B is 67.5, what is the value of A – B?
Option 1: 10
Option 2: 18
Option 3: 12
Option 4: 15
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Correct Answer: 15
Solution : The ratio of 45% of 80% of A to 30% of 40% of B is 15 : 4. The average of A and B is 67.5. According to the question, $\frac{\frac{45}{100}\times\frac{80}{100}\times \text{A}}{\frac{30}{100}\times\frac{40}{100}\times \text{B}} = \frac{15}{4}$ ⇒ $\frac{3\text{A}}{\text{B}} = \frac{15}{4}$ ⇒ $\frac{\text{A}}{\text{B}} = \frac{5}{4}$ So, take A = 5x and B = 4x Sum of A and B = 67.5 × 2 = 135 ⇒ 5x + 4x = 135 ⇒ 9x = 135 ⇒ x = 15 $\therefore$ A – B = 5x – 4x = x = 15 Hence, the correct answer is 15.
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