Question:
The ratio of the number of boys and the girls in a group is 5 : 8. If 4 more girls join the group and 5 boys leave the group, then the ratio of the number of boys to the number of girls becomes 1 : 2. Originally, what was the difference between the number of boys and girls in the group?
The ratio of the number of boys and the girls in a group is 5 : 8. If 4 more girls join the group and 5 boys leave the group, then the ratio of the number of boys to the number of girls becomes 1 : 2. Originally, what was the difference between the number of boys and girls in the group?
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Translate ratios to variables, then use the new condition to form an equation and solve.
Updated On: Apr 24, 2025
- 21
- 24
- 27
- 30
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The Correct Option is A
Solution and Explanation
Let the number of boys = \( 5x \), girls = \( 8x \)
After changes:
Boys = \( 5x - 5 \), Girls = \( 8x + 4 \)
\[
\frac{5x - 5}{8x + 4} = \frac{1}{2}
\Rightarrow 2(5x - 5) = 8x + 4
\Rightarrow 10x - 10 = 8x + 4
\Rightarrow 2x = 14 \Rightarrow x = 7
\]
So, Boys = 35, Girls = 56
Difference = \( 56 - 35 = 21 \)
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