Question

The L.C.M of two numbers is 455 and their H.C.F is 5. If the sum of the numbers is 100, then their difference is?

1. 6
2. 4
3. 50
4. 30
5. 60

Answer 1

Correct Answer - Option 4 : 30

Given:

L.C.M of two numbers = 455

H.C.F of two numbers = 5

Sum of the two numbers = 100

Calculation:

Let the numbers be x and (100 - x) respectively.

⇒ x(100 – x) = 5 × 455

⇒ 100x – x² = 2275

⇒ x² – 100x + 2275 = 0

⇒ (x – 65)(x – 35) = 0

⇒ x = 65, 35

The difference of these numbers = 65 – 35

⇒ 30

∴ The difference of these numbers is 30.