2026 · Q17
The product of two numbers is 1050. The quotient when the larger number is divided by the smaller number is 4 and the remainder is 10. What is the sum of the two numbers?
Elementary MathematicsNumber System
- A70
- B75
- C80
- D85
Explanation
Let the numbers be x > y with xy = 1050 and x = 4y + 10. Substituting gives y(4y + 10) = 1050, i.e. 4y² + 10y − 1050 = 0 or 2y² + 5y − 525 = 0. The discriminant is 25 + 4200 = 4225 = 65², so y = (−5 + 65)/4 = 15 and x = 4·15 + 10 = 70. Their sum is 85, option D.