The sum of two numbers is 119 and their HCF is 17 and LCM is 170, so t

1.	The sum of two numbers is 119 and their HCF is 17 and LCM is 170, so the inverse sum of the numbers is ______.A. 119/501B. 501/119C. 7/170D. 170/71. A2. C3. B4. D
Answer» 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.

The sum of two numbers is 119 and their HCF is 17 and LCM is 170, so the inverse sum of the numbers is ______.A. 119/501B. 501/119C. 7/170D. 170/71. A2. C3. B4. D

Answer» 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.

Discussion

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