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After the first round of counselling, the ratio of the filled seats to the unfilled seats in a college is 7 ∶ 3. If there were 60 more seats in the college, and 24 more seats remained unfilled, then the ratio of filled to unfilled seats would be 9 ∶ 4. How many seats are there in the college?

After the first round of counselling, the ratio of the filled seats to the unfilled seats in a college is 7 ∶ 3. If there were 60 more seats in the college, and 24 more seats remained unfilled, then the ratio of filled to unfilled seats would be 9 ∶ 4. How many seats are there in the college? Correct Answer 720

Let the number of filled and unfilled seats in the college be ‘7x’ and ‘3x’ respectively

⇒ Total no. of seats in college = 7x + 3x = 10x

Now, if there were 60 seats more in college,

⇒ Total no. of seats would be = 10x + 60

⇒ No. of unfilled seats = 3x + 24

⇒ No. of filled seats = Total seats - Unfilled seats = 10x + 60 - 3x - 24 = 7x + 36

∵ The ratio of filled to unfilled seats would be 9 ∶ 4

⇒ (7x + 36) / (3x + 24) = 9/4

⇒ 28x + 144 = 27x + 216

⇒ x = 216 - 144 = 72

∴ Total no. of seats in college = 10x = 10(72) = 720

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