# The L.C.M. of two numbers is 495 and their HCF is 5. If the sum of the two numbers is 100 then their difference is

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Telangana Police SI Mains Exam 2016 Official Paper 1
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1. 10
2. 46
3. 70
4. 90

Option 1 : 10
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Telangana Police SI Preliminary Exam 2018 Official Paper 1
660
200 Questions 200 Marks 180 Mins

## Detailed Solution

Given:

The L.C.M. of two numbers is 495 and their HCF is 5.

The sum of the two numbers is 100

Formula used:

Product of the two number = LCM × HCF

Calculation:

Let the one number be x and another number be 100 - x

According to the question,

⇒ x(100 - x) = 495 × 5

⇒ 100x - x2 = 2475

⇒ x2 - 100x + 2475 = 0

⇒ x2 - 55x - 45x + 2475 = 0

⇒ x(x - 55) - 45(x - 55) = 0

⇒ (x - 55)(x - 45) = 0

⇒ x = 55 or 45

If one number is 45 then another number 100 - 45 = 55

Or one number is 55 then another number 100 - 55 = 45

Their difference is 55 - 45 = 10

∴ Their difference is 10.
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