Question

The sum of the digits of a 2-digit number is 10. The number obtained by
interchanging the digits exceeds the original number by 36. Find the original (linear equation in one variable)​

Answer 1

Given :

• Sum of two digit number = 10
• The number obtained by interchanging the digits exceeds the original by 36.

To find :

• The original number.

According to the question :

• Let one's digit be 'y'
• And tense digit be 'x'

It is given that sum of two digit number is 10.

• x + y = 10 -----(1)

We know that, x denotes the tense place digit. Therefore, it will be '10x + y'.

When we interchange it will be '10y + x'. And it exceeds the original number by 36.

The original number is 10x + y. Therefore,

10 y + x = (10x + y) + 36

⟹ (10y - y) - (10x - x) = 36

⟹ 9y - 9x = 36

⟹ y - x = 4 -------(2)

Adding (1) & (2) :

x + y = 10

y - x = 4

_______

2y = 14

_______

[ (+x) and (-x) will get cancelled ]

⟹ 2y = 14

⟹ y = 14 / 2

⟹ y = 7

Substituting 'y' in (1) :

⟹ x + y = 10

⟹ x + 7 = 10

⟹ x = 10 - 7

⟹ x = 3

• ∴ The original number is = 37