If the sum of two numbers is 35 and the LCM and HCF of the same numbers are 60 and 5 respectively. The value of larger number is:
If the sum of two numbers is 35 and the LCM and HCF of the same numbers are 60 and 5 respectively. The value of larger number is:
1). 25
2). 10
3). 12
4). 20
1 answers
Let the larger number be x and smaller number be y,
⇒ x + y = 35
⇒ y = 35 – x ----(1)
LCM (x, y) = 60
HCF (x, y) = 5
As, LCM (x, y) × HCF (x, y) = x × y
⇒ 60 × 5 = x × (35 – x) ----[? substituting the value of Eq(2)]
⇒ 300 = 35x – x2
⇒ x2 – 35x + 300 = 0
⇒ x2 – 15x – 20x + 300 = 0
⇒ (x – 15) (x – 20) = 0
Because x is larger number,
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