Question

the sum of digits of a two digit is 8.the difference between the number and that formed by reversing the digits 18 find the number​

Answer 1

GIVEN:

• The sum of digits of a two digit is 8.
• The difference between the number and that formed by reversing the digits 18.

LET:

• The digit at unit place be x.
• The digit at tens place be y.
• Number = 10y + x

THEN:

Number formed by reversing the digits = $\sf 10y + x$

$\underbrace{According\:to\:the\:question}$

$\longrightarrow \sf\: x+y=8.......(1) \\ \\ \longrightarrow \sf\:(10y+x)-(10x+y)=18 \\ \\ \longrightarrow \sf\: 9(y-x)=18 \\ \\ \longrightarrow \sf\: y-x=2......(2)$

By solving (1) and (2), we get :-

$\longrightarrow \sf\: \cancel{x}+y+y-\cancel{x}=8+2 \\ \\ \longrightarrow \sf\: 2y=10 \\ \\ \longrightarrow \sf\:y=5$

Putting the value of y in (1)

$\longrightarrow \sf\:x+5=8\\ \\ \longrightarrow \sf\:x=8-5\\ \\ \longrightarrow \sf\:x=3$

Hence, the number is,

$\longrightarrow \sf\: 10y + x \\ \\ \longrightarrow \sf\: (10 \times 5) + 3 \\ \\ \implies \sf\: 53$

Number = $\boxed{53}$

Answer 2

Given :

• The sum of digits of a two digit is 8.

• The difference between the number and that formed by reversing the digits 18.

To find :

• The number =?

Step-by-step explanation :

Let the ones digit of two digits number be, x.

Then, the ten's digit of two digits number be 8 - x.

So, the number is, 10(8 - x + x) = 80 - 9x

After reversing the digits the number will be, 10 x+ (8 - x) = 9x + 8

According to the question :

➮ 80 - 9x = 9x + 8 + 18

➮ 18x = 80 - 8 - 18

➮ 18x = 54

➮ x = 54/18

➮ x = 3

Hence,

Once digit, x = 3

Tens digit, 8 - x = 8 - 3 = 5.

Therefore, the number will be, 10 × 5 + 3 = 53.