240 students are arranged in equal rows. If the number of rows is reduced by 4, each row will have 5 more students. What was the original number of rows?
Answer and explanation
Correct answer: 16
Let the original number of rows be x. Then each row initially contains 240/x students. After reducing the rows by 4, each row contains 240/(x − 4) students. The condition gives 240/(x − 4) − 240/x = 5, where x > 4. Simplifying, 960/[x(x − 4)] = 5, so x(x − 4) = 192 and x² − 4x − 192 = 0. Factorisation gives (x − 16)(x + 12) = 0. Since the number of rows must be positive, x = 16. Option C is correct. Checking, 240/16 = 15 students per row; with 12 rows, 240/12 = 20, which is exactly 5 more. The other options fail this comparison.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Let the original number of rows be x. Then each row initially contains 240/x students. After reducing the rows by 4, each row contains 240/(x − 4) students. The condition gives 240/(x − 4) − 240/x = 5, where x > 4. Simplifying, 960/[x(x − 4)] = 5, so x(x − 4) = 192 and x² − 4x − 192 = 0. Factorisation gives (x − 16)(x + 12) = 0. Since the number of rows must be positive, x = 16. Option C is correct. Checking, 240/16 = 15 students per row; with 12 rows, 240/12 = 20, which is exactly 5 more. The other options fail this comparison.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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