Question

The sum of the digits of a two-digit number is 14. If 36 is added to the number, its digits are interchanged. Find the number

Answer 1

Answer:

59

Step-by-step explanation:

Assume the two digit number is 10x+ y

1st equation : x+y = 14

2nd equation : 10x + y +36 = 10y + x

solving the two equations we get x=5 and y=9

hence the number is 59

Answer 2

Step-by-step 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