Question : The sum of the two numbers is 45. Their HCF and LCM are 5 and 70 respectively. Find the sum of the reciprocal of the two numbers.
Option 1: $\frac{9}{70}$
Option 2: $\frac{3}{140}$
Option 3: $\frac{4}{35}$
Option 4: $\frac{3}{16}$
Correct Answer: $\frac{9}{70}$
Solution :
Let the numbers be a and b
⇒ a + b = 45
and, a × b = HCF × LCM = 5 × 70 = 350
⇒ $\frac{1}{a}$ + $\frac{1}{b}$ = $\frac{a + b}{350}$ = $\frac{45}{350}$ = $\frac{9}{70}$
Hence, the correct answer is $\frac{9}{70}$.
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