Subject: General Aptitude · Chapter: H.C.F. and L.C.M. of Numbers · Exam: · Marks: · Difficulty:
The L.C.M. of two numbers is 495 and their H.C.F. is 5. If the sum of the numbers is 10, then their difference is
(a)10
(b)46
(c)70
(d)90
Answer
Answer (as printed): A
Explanation
Let the numbers be $x$ and $(100-x)$. Then, $\quad x(100-x)=5 \times 495$ $\Leftrightarrow x^{2}-100 x+2475=0$ $\Leftrightarrow \quad(x-55)(x-45)=0$ $\Leftrightarrow \quad x=55$ or $x=45$. ∴ The numbers are 45 and 55. Required difference $=(55-45)=10$.
Explanation as extracted from the printed page; notation may be imperfect.