Question

A number has two digits whose sum is 14 .If 36 is added to the number, its digits are interchanged . The number is

Answer 1

First digit = a
Other digit = 14-a
No. = 10(14 - a) +a
= 140 - 10a + a
= 140 - 9a

On interchanging the digits
No. = 10(a) +14-a
= 10a + 14 - a
=9a +14

A.T.Q.

Answer 2

Explanation:

Let the Digit in the units place of the Two Digit number be : A

Given : The Sum of the Digits of Two Digit number is 14

It means : The Digit in the Ten's place will be : 14 - A

★  The Two Digit Number can be written as : 10(14 - A) + A

Given : If 36 is added to the number, the Digits get interchanged

$\mathsf{\implies 10(14 - A) + A + 36 = 10(A) + (14 - A)}$

$\mathsf{\implies 140 - 10A + A + 36 = 10A + 14 - A}$

$\mathsf{\implies 176 - 9A = 9A + 14}$

$\mathsf{\implies 9A + 9A = 176 - 14}$

$\mathsf{\implies 18A = 162}$

$\mathsf{\implies A = 9}$

$\mathsf{\implies Ten's\;Place\;Digit = (14 - 9) = 5}$

Answer : The Two Digit Number is 59