Question

The sum of the digit of two digit number is 7. Often number formed, by reversing the digit is less than the original number by 27, find the original number.

Answer 1

Answer:

52

Step-by-step explanation:

Given :

The sum of the digit of two digit number is 7.

Often number formed, by reversing the digit is less than the original number by 27,

find the original number.

Solution :

Let the digits be xy ,..

x be in 10s digit & y be in 1s digit,.

so, the number is defined as (in expanded form ) = 10x + y,

Statement 1 :

The sum of the digit of two digit number is 7.

⇒ x + y = 7 ...(i)

Statement 2 :

Often number formed, by reversing the digit is less than the original number by 27,

⇒ Original number - reversed number = 27

⇒ xy - yx = 27 (in digit form)

⇒ (10x - y) - (10y + x) = 27 (in expanded form),

⇒ 10x - y - 10y - x = 27

⇒ 9x - 9y = 27

⇒ 9 × (x - y) = 9 × 3

⇒ x - y = 3 ...(ii)

By adding (i) & (ii),

We get,

⇒ (x + y) + (x - y) = 7 + 3

⇒ x + x + y - y = 10

⇒ 2x = 10

⇒ 2x = 5 × 2

⇒ x = 5 ,..

By substituting value of x in (i),

We get,

⇒ x + y = 7

⇒ 5 + y = 7

⇒ y = 7 - 5

⇒ y = 2,.

Then, the number is 10x + y = 5 × 10 + 2 = 50 + 2 = 52