Question

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?

• A. 1000
• B. 1100
• C. 1200
• D. 1300

Answer 1

The Correct Option is D

To find the total number of students in the college in June-2020, we need to analyze the given ratios and their conditions.

1. 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 \(2x\). 
2. Thus, the total number of students in June-2020 is:
   • Total = \((3x + 2x) = 5x\)
3. In September-2020, there are 80 fewer boys and 20 fewer girls.
   • Number of boys in September = \((3x - 80)\)
   • Number of girls in September = \((2x - 20)\)
4. The new ratio is given as 7:5. Hence, we can set up the equation:
   • \(\frac{3x - 80}{2x - 20} = \frac{7}{5}\)
5. Cross-multiply to solve for \(x\):
   • \(5(3x - 80) = 7(2x - 20)\)
   • \(15x - 400 = 14x - 140\)
   • \(15x - 14x = 400 - 140\)
   • \(x = 260\)
6. 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.