Question

9. A number consists of two digits whose sum is 8. If 18
is added to the number, its digits are reversed. Find
the number.
​

Answer 1

To Find:-

• Find the number.

Given:-

• A number consists of two digits whose sum is 8.
• If 18 is added to the number, its digits are reversed.

Solution:-

Let the unit digit be " x "

Then, 10th digit be " 8 - x "

So,

$\tt\implies \: 10( 8 - x ) + x$

$\tt\implies \: 80 - 10x + x$

$\tt\implies \: 80 - 9x$

The number is reversed.

$\tt\implies \: 10x + ( 8 - x )$

$\tt\implies \: 10x + 8 - x$

$\tt\implies \: 9x + 8$

According to the Question:

$\tt\implies \: ( 80 - 9x ) + 18 = 9x + 8$

$\tt\implies \: 80 - 9x + 18 = 9x + 8$

$\tt\implies \: 98 - 9x = 9x + 8$

$\tt\implies \: 98 - 8 = 9x + 9x$

$\tt\implies \: 18x = 90$

$\tt\implies \: x = \cancel\dfrac { 90 } { 18 }$

$\tt\implies \: x = 5$

Hence,

The number is

$\tt\implies \: 80 - 9x$

$\tt\implies \: 80 - 9( 5 )$

$\tt\implies \: 80 - 45$

$\tt\implies \: 35$

∴ The number is 35.

Answer 2

Answer:☞

Hello Friend !

Let us assume that one of the digit of the two digit number is X, then problem the other number will be (8 - X)

From problem we get that, if we add 27 to the number the digits get interchanged and also since the number is a two digit number then X will in tens place (7 - X) will be in ones place.

So the equation we get

10X + (8 - X) + 18 = 10(8 - X) + X

10X + 8 - X + 18 = 80 -10X + X

9X + 26 = 80 - 9X

9X + 9X = 80 - 26

18X = 54

X = 54/18

X = 3,

So the digit in tens place = 3 the digit in ones place is (8 - 3 = 5) , then the number is 35 and when 18 is added the result is 53, the digits interchange their position in the new number.

Ans: 35.

Hope this helps !!