Question

The ratio of the number of boys and girls in a college is 5 : 4, if the percentage decrease in the number of boys is 30% and the percentage increase in the number of girls is 5%. The new ratio will be:

• A. 5 : 6
• B. 6 : 5
• C. 5 : 9
• D. 9 : 4

Hint:

In ratio problems involving percentage changes, apply the percentage increases or decreases directly to the quantities and then simplify the resulting ratio.

Answer 1

The Correct Option is A

Let the number of boys be \( 5x \) and the number of girls be \( 4x \). Step 1: Calculate the new number of boys and girls. - The number of boys after a 30% decrease will be: \[ \text{New number of boys} = 5x - 0.30 \times 5x = 0.70 \times 5x = 3.5x \] - The number of girls after a 5% increase will be: \[ \text{New number of girls} = 4x + 0.05 \times 4x = 1.05 \times 4x = 4.2x \]

Step 2: Find the new ratio of boys to girls. The new ratio of boys to girls is: \[ \frac{3.5x}{4.2x} = \frac{3.5}{4.2} = \frac{5}{6} \] Thus, the new ratio is \( 5 : 6 \). Final Answer: The correct answer is (a) 5 : 6.