Question

The sum of the digits of two digit number is 8 . If digit are reversed then new number is formed increased by 18 Find the number.

Answer 1

Given:

• Sum of two digits of two digit number is 8.
• If digits are reversed then number formed increased by 18.

To Find:

• The number

Solution:

Let the digits in tens place be "x".

And the digits in unit place be "y".

Therefore,

• The original two digits number is 10x + y.

According to the first condition:

Sum of digits of a two digit number is 8.

→ x + y = 8 --(1)

According to the second condition:

The new number increased by 18, when the digits are reversed.

→ 10y + x = 10x + y + 18

→ 10y - x = 10x - y + 18

→ 9y = 9x + 18

→ 9y - 9x = 18

→ y - x = 2

→ x - y = -2 --(2)

On solving (1) and (2) we get,

→ x + y = 18

→ x - y = -2

→ 2x = 6

→ x = 3

Substituting x = 3 in (1),

We get,

→ x + y = 8

→ 3 + y = 8

→ y = 8 - 3

→ y = 5

So,

→ 10x + y

→ 10(3) + 5

→ 30 + 5

→ 35

Hence, the original number is 35.