LCM and HCF of two numbers are 90 and 15, respectively. If the sum of the two numbers is 75, then find the greater number.
Answer & explanation
Correct answer: option 1
LCM and HCF of two numbers are 90 and 15, respectively.
The sum of the two numbers is 75
LCM × HCF = Product of two numbers
Let one number be x
Other number = (75 - x)
Then,
⇒ 90 × 15 = x(75 - x)
⇒ 1350 = 75x - x2
⇒ x2 - 75x + 1350=0
⇒ x2- 45x - 30x + 1350=0
⇒ x = 45, 30
∴ Greater number = 45