3611. The ratio of boys and girls in a class was 11:13. 8 girls and 4 boys join the class from this academic year and the ratio becomes 4:5. Find the strength of the class?
- A. 104
- B. None of these
- C. 112
- D. 108
Check answer and explanation
Answer: 108
Explanation Let's break down the problem step by step: Step 1: Express the initial number of boys and girls using the given ratio Let the number of boys be 11x and the number of girls be 13x. Step 2: Calculate the new number of boys and girls after 4 boys and 8 girls join the class New number of boys = 11x + 4 New number of girls = 13x + 8 Step 3: Set up the equation based on the new ratio Given the new ratio is 4:5, we can write the equation as: (11x + 4) / (13x + 8) = 4/5 Step 4: Solve the equation Cross-multiplying gives us: 5(11x + 4) = 4(13x + 8) 55x + 20 = 52x + 32 55x - 52x = 32 - 20 3x = 12 x = 4 Step 5: Calculate the strength of the class Strength of the class = Initial number of boys + Initial number of girls + New boys + New girls = 11x + 13x + 4 + 8 = 24x + 12 = 24*4 + 12 = 96 + 12 = 108