In a two digit number the sum of the digits is 9. Also, when 27 is subtracted from the number the digits are reversed. Find the number?

In a two digit number the sum of the digits is 9. Also, when 27 is subtracted from the number the digits are reversed. Find the number?

Solutions

Expert Solution

Solution:

If we consider the digits at the unit's place and at the ten's place be x and y respectively,

then the given number = 10 y + x

Also, the digits are reversed when 27 is subtracted from the above number.

So,

10 y + x - 27 = 10x + y

⇒ 10y-y-27 = 10x-x

⇒ 9y-27 = 9x

⇒ 9y-9x = 27

⇒ y-x = 3 - Eq. I

Also given:

x+y = 9 - Eq. II

Adding Eq. I and Eq. II:

2y = 12 ⇒ y = 12/2 = 6

From Eq. II,

x = 9-y

⇒ x = 9-6 = 3

Thus, the number is 10(6) + 3 = 63

The number is 10(6) + 3 = 63

Shams answered 1 year ago

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