SSC GD 2021 PYQ — Question 70

The correct answer is option 3 i.e. 18

Given:

The LCM and HCF of two numbers are 420 and 6. Sum of the numbers is 102

Formula used:

LCM × HCF = a × b          ---- (1)

(a + b)² = a² + b² + 2ab              ---- (2)

(a - b)² = a² + b² - 2ab            ---- (3)

Where a and be are two numbers

Calculations:

Let a and be the two numbers

Using equation (1), we get

⇒ LCM × HCF = a × b

⇒ a × b = 2520

Using equation (2),

⇒ (102)² = a² + b² + 2 × 2520

⇒ 10404 = a² + b² + 5040

⇒ a² + b² = 10404 - 5040

⇒ a² + b² = 5364

Putting the above value in equation (3)

⇒ (a - b)² = 5364 - 5040

⇒ (a - b)² = 324

⇒ (a - b) = 18