Question

The sum of the digits of a two digit number is 8.The number obtained by interchanging the two digits exceeds the given number by 36.Find the number?

Answer 1

Answer:

26

Step-by-step explanation:

Let the two digits number be = 10x + y having x and y as digits in tens and unit position

Given that, sum of the digits of a two digit number is 8,

Hence, x + y = 8......................................eq(1)

Also, the number obtained by interchanging the two digits exceeds the given number by 36,

Hence, 10y + x = 10x + y + 36

or, 10x + y - 10y - x + 36 =0

or, 9x - 9y + 36 = 0

or, x - y + 4 = 0

or, x - y = -4......................................eq(2)

Adding, eq(1) and eq(2)

x + y + x - y = 8 + (-4)

or, 2x = 4

or, x = 2

Putting x = 2 in eq(1)

We have, y = 6

Hence, The Number is (10 x 2) + 6 = 26

Answer 2

Answer:

$\huge\star{\red{Q}{uestion}}\star\:$

Sum of the digits of a two-digit number is 12. The given number exceeds the number obtained by interchanging the digits by 36. Find the given

number.

$\huge\star{\red {A}{nswer}}\star\:$

$\huge\underline {Let,}$

The tens digit of the required number be x

and the units digit be y

\huge\underline {Then,}

Then,

x + y = 12 ......... eq. (1)

Required number = (10x + y)

Number obtained on reversing the digits = (10y + x)

$\huge\underline {Therefore,}$

(10y + x) - (10x + y) = 18

9y - 9x = 18

x - y = 12 ......... eq. (2)<br>

On adding eq. (1) and eq. (2)

$\huge\underline {We\: get}$

x + y + y - x = 12 +2

2y = 14

y = 2

$\huge\underline {Therefore}$

x = 5

Hence, the required number is 57

$\huge\green { Hope\: this\: helps\: you}$