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?
- 108
- 104
- 112
- None of these
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
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