Question

In a class there are 48 students. The ratio of number of boys to number of girls is 5:3. The number of girls to be added to the class so that the number of boys to girls is 6:5 is?

• A. 7
• B. 6
• C. 12
• D. 17

Hint:

Use ratio formulas and cross multiplication to solve problems involving changes in ratios.

Answer 1

The Correct Option is A

Step 1: Calculate current number of boys and girls
Ratio = 5:3
Total students = 48
Sum of ratio parts = 5 + 3 = 8
- Number of boys = (5/8) × 48 = 30
- Number of girls = (3/8) × 48 = 18
Step 2: Let the number of girls to be added = x
After adding x girls, new number of girls = 18 + x
Number of boys remains 30
Step 3: New ratio of boys to girls = 6:5
\[ \frac{30}{18 + x} = \frac{6}{5} \] Cross multiply:
5 × 30 = 6 × (18 + x)
150 = 108 + 6x
6x = 150 - 108 = 42
x = 7
Thus, Option (A) 7 is correct.