Correct Answer - Option 2 : C
Given:
HCF = 17
LCM = 170
Sum of two numbers = 119
Concept used:
Product of two numbers = LCM × HCF
Calculation:
Let the two numbers be 'a' and 'b'.
⇒ a + b = 119
⇒ a = 119 - b
Product of two numbers = LCM × HCF
⇒ a × b = LCM × HCF
⇒ a × (119 - b) = 17 × 170
⇒ 119a - a2 = 2890
⇒ a2 - 119a + 2890 = 0
⇒ a = 34, 85
When a = 34, then b = 85
When a = 85, then b = 34
The possible value of a and b is 84 and 34.
Sum of inverse of a and b
⇒ (1/84) + (1/34)
⇒ 7/170
∴ The sum of inverse is 7/170.