If the ratio of two numbers is 17 : 7 and the product of their LCM and their HCF is 119, then the sum of the reciprocals of the LCM and the HCF is:

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RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 3)
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  1. \(\frac{120}{139}\)
  2. \(\frac{120}{137}\)
  3. \(\frac{120}{119}\)
  4. \(\frac{120}{161}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{120}{119}\)
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Detailed Solution

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Given:

The ratio of two numbers is 17:7.

The product of their LCM and HCF is 119.

Formula used:

Product of two numbers = LCM × HCF

Sum of reciprocals of LCM and HCF = (1/LCM) + (1/HCF)

Calculation:

Let the two numbers be 17x and 7x.

Product of two numbers = 17x × 7x = 119x²

⇒ LCM × HCF = 119

LCM × HCF = Product of two numbers

⇒ 119x² = 119

⇒ x² = 1

⇒ x = 1

⇒ Numbers are 17x = 17 and 7x = 7.

LCM of 17 and 7 = 119

HCF of 17 and 7 = 1

Sum of reciprocals of LCM and HCF = (1/LCM) + (1/HCF)

⇒ Sum = (1/119) + (1/1)

⇒ Sum = 120/119

∴ The correct answer is option (3).

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