Question
The HCF and LCM of two numbers, A and B, are 15 and 225,
respectively. Additionally, the difference between the two numbers is 35. Find the sum of these two numbers.Solution
ATQ,
HCF (A, B) = 15
LCM (A, B) = 225
We know that,
HCF (A, B) × LCM (A, B) = A × B
Also, A – B = 35
Or, B = A – 35
ATQ:
A × (A – 35) = 15 × 225
Or, A² – 35A = 3375
Or, A² – 35A – 3375 = 0
Or, A² – 75A + 40A – 3375 = 0
Or, A(A – 75) + 40(A – 75) = 0
Or, (A – 75)(A + 40) = 0
So, A = 75 or A = -40
Since, A cannot be negative, we discard A = -40.
So, A = 75
And, B = 75 – 35 = 40
Therefore, required sum = (75 + 40) = 115
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