In June-2020, the ratio of boys to girls in a college was 3:2. In September-2020, there were 80 fewer boys and 20 fewer girls in the college and the ratio of boys to girls was 7:5. What was the total number of students in the college in June-2020?
- 1000
- 1100
- 1200
- 1300
The Correct Option is D
Solution and Explanation
To find the total number of students in the college in June-2020, we need to analyze the given ratios and their conditions.
- In June-2020, the ratio of boys to girls is given as 3:2. Let the number of boys be \(3x\) and the number of girls be \(2x\).
- Thus, the total number of students in June-2020 is:
- Total = \((3x + 2x) = 5x\)
- In September-2020, there are 80 fewer boys and 20 fewer girls.
- Number of boys in September = \((3x - 80)\)
- Number of girls in September = \((2x - 20)\)
- The new ratio is given as 7:5. Hence, we can set up the equation:
- \(\frac{3x - 80}{2x - 20} = \frac{7}{5}\)
- Cross-multiply to solve for \(x\):
- \(5(3x - 80) = 7(2x - 20)\)
- \(15x - 400 = 14x - 140\)
- \(15x - 14x = 400 - 140\)
- \(x = 260\)
- Substitute \(x=260\) back into the expression for total students in June-2020:
- Total students in June-2020: \(5x = 5 \times 260 = 1300\)
Therefore, the total number of students in the college in June-2020 was 1300.
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