2020 · Q31
Students of a class are made to sit in rows of equal number of chairs. If number of students is increased by 2 in each row, then the number of rows decrease by 3. If number of students is increased by 4 in each row, then the number of rows decreases by 5. What is the number of students in the class?
Elementary MathematicsAlgebra
- A100
- B105
- C110
- D120
Explanation
Let there be r rows of c chairs: (c + 2)(r − 3) = rc gives 2r − 3c = 6, and (c + 4)(r − 5) = rc gives 4r − 5c = 20. Solving: from the first, 2r = 6 + 3c; substituting gives 12 + 6c − 5c = 20, so c = 8 and r = 15. The hall has 15 × 8 = 120 chairs.