Question

the sum of the digits of a two number is 14.the difference between this number and the number obtained on reserving the digits is 18.find the number ​

Answer 1

Answer:

The number is 68

Step-by-step explanation:

Let the digits of the two - digit number be x and y

Therefore , the number is

10x + y

The sum of the digits is 14

$x + y = 14 - - - (1)$

And the difference between this number and the number obtained on reversing the digit is 18

$10y + x - (10x + y) = 18 \\ \implies10y + x - 10x - y = 18 \\ \implies9y - 9x = 18 \\ \implies9(y - x) = 18 \\ \implies \: y - x = 2 \\ \implies \: y = 2 + x - - - (2)$

Now , from equation (1)

$x + 2 + x = 14 \\ \implies2x = 14 - 2 \\ \implies2x = 12\\ \implies \: x = 6$

Again , from equation (2) we have

$y = 2 + 6 \\ \implies \: y = 8$

So , the original number is

$10 \times 6 + 8 \\ = 60 + 8 \\ = 68$

Answer 2

Linear Equations :

Let the one's place digit be x and ten's place digit be y.

Number = 10y + x

x + y = 14 --> ( i )

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

9y - 9x = 18

y - x = 2 --> ( ii)

Adding ( i ) & ( ii ),

2y = 16

y = 8

Putting value of 'y' in ( i ),

x + 8 = 14

x = 6

Number = 10* 8 + 6 = 86

Number = 86