Question
The HCF and LCM of two numbers, A and B, are 14 and 196,
respectively. The difference between these two numbers is 28. Find their sum.Solution
ATQ,
HCF (A, B) = 14
LCM (A, B) = 196
We know that,
HCF (A, B) × LCM (A, B) = A × B
Also, A – B = 28
Or, B = A – 28
ATQ:
A × (A – 28) = 14 × 196
Or, A² – 28A = 2744
Or, A² – 28A – 2744 = 0
Or, A² – 56A + 28A – 2744 = 0
Or, A(A – 56) + 28(A – 56) = 0
Or, (A – 56)(A + 28) = 0
So, A = 56 or A = -28
Since, A cannot be negative, we discard A = -28.
So, A = 56
And, B = 56 – 28 = 28
Therefore, required sum = (56 + 28) = 84
799.99 + 1500.12 ÷ 29.98 × 50.01 = ? × 24.96
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