Question

sum of a digits of a two digit number is 15. when we interchange the digits it is found that the resulting digit is greater than the original number by 27. what is the original number.

Answer 1

Answer :-

The original number is 69.

Solution :-

Let the digits of the tow digit number be x and y

Sum of digits = 15

⇒ x + y = 15 ---eq(1)

Original number = 10x + y

Number when digits are interchanged = 10y + x

Given

Number when digits are interchanged - Original number = 27

⇒ 10y + x - (10x + y) = 27

⇒ 10y + x - 10x - y = 27

⇒ 9y - 9x = 27

⇒ 9(y - x) = 27

⇒ y - x = 27/9

⇒ y - x = 3

Adding eq(1) & eq(2)

⇒ x + y + (y - x) = 15 + 3

⇒ x + y + y - x = 18

⇒ 2y = 18

⇒ y = 18/2

⇒ y = 9

Substitute y = 6 in eq(1)

⇒ x + y = 15

⇒ x + 9 = 15

⇒ x = 15 - 9

⇒ x = 6

Original number = 10x + y

= 10(6) + 9

= 60 + 9

= 69

Therefore the original number is 69.

Answer 2

$\Large\bold{\underline{\underline{Answer:-}}}$

$\Large\bold{\boxed{\boxed{69 }}}$

$\rule{200}{4}$

$\bf\small\bold{\underline{\underline{Step-By-Step\:Explanation:-}}}$

Let digit in unit's place be x

then digit in ten's place is 15 - x (given the sum of the digits is 15)

⇒10x + (15 - x) = 9x + 15

when digits are interchanged, the new number is

⇒10(15-x) + x = 150 - 9x

according to the question the new number is 27 more than the original number

therefore: 150 - 9x = 9x + 15 + 27

⇒150 - 9x = 9x + 42

⇒150 - 42 = 9x + 9x

⇒108= 18x

or x = 6

the original number was 10x + (15 - x)

on substituting the value of x

⇒10 × 6 + (15 - 6)

⇒60 + 9

⇒69

Threrefore, the two digit number 69