Question

The sum of the digits of a two - digit number is 4 . The number got by interchanging the digits is 18 less than the original number . what is the number . ? ​

Answer 1

$\huge\mathfrak\red{Answer:-}$

31

$\mathfrak\purple{Step \: by \: stiep \: explanation:-}$

x + y = 4

10x + y - 18 = 10y + x

9x - 18 = 9y

x - y = 2

x + y = 4

x - y = 2

thus, 2x = 6 orx = 3

x - y = 2

3 - y = 2

y = 1

so, number is 10(3) + 1 or 31

_divide by 9

check

13( digits interchanged) is 18 less than 31

Answer 2

Answer:

• The Original Number is 31.

Step-by-step explanation:

Given,

• The sum of the digits of a two - digit number is 4.
• The number got by interchanging the digits is 18 less than the original number.

To Find,

• The original number.

Solution,

Let's,

• The tenth-digit of number = x

And,

• The unit digit of number = y

The Original Number = 10x + y

After Interchanging the Digits,

• The tenth-digit of number = y

And,

• The unit digit of number = x

The Interchanged number = 10y + x

According To Question,

Situation 1,

The sum of digits is 4.

So,

$:\implies\tt x + y = 4 \: \: \: ...(1)$

Situation 2,

$:\implies\tt (Original \: \:Number) - (Interchanged \: \: Number) = 18 \\ \\ :\implies\tt (10x + y) - (10y + x) = 18 \\ \\ :\implies\tt 9x - 9y = 18 \\ \\ :\implies\tt x - y = 2 \: \: \: ...(1)$

By Elimination Method,

Adding Eq [1] and Eq [2] to eliminate y,

$:\implies\tt (x + y) + (x - y) = 4 + 2 \\ \\:\implies\tt x + y + x - y = 6 \\ \\ :\implies\tt 2x = 6 \\ \\ :\implies \color{red} \boxed{\tt x = 3}$

Substituting this value of x in Eq [1],

$:\implies\tt x + y = 4 \: \: \: ...(1) \\ \\ :\implies\tt 3 + y = 4 \\ \\ :\implies \color{red} \boxed{\tt y = 1}$

Hence, x = 3 and y = 1

The Original Number = 10x + y

• ➤ The Original Number = 10(3) + 1
• ➤ The Original Number = 31

Required Answer,

• The Original Number is 31.