Question

The sum of the 2 digit number is 15. The number obtained by reversing the digit is 9 less than the original number. Find the number​

Answer 1

Let the numbers be x and y.

Therefore,

x + y = 15 ............1st eq

10y + x = 10x + y +9

9y - 9x = 9

Y - x = 1 ......................... 2nd Eq.

Now,

x + y = 15

- x + y = 1 ( 2nd equation )

=) 2y = 16

=) y = 8

Then, put the value of y in the equation.

we get,

x + 8 = 15

=) x = 15 - 8

=) x = 7

Two digit no. is 87

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Answer 2

The sum of the two digits (Let the digits be x each) : 15

x + x = 15

x = 15 - x

Thus, one digit will be x and other (15-x).

Original number – 10(x) + (15-x)

= 10x + 15 - x = 9x + 15

Number after reversing the digits – 10(15 - x) + x

= 150 - 10x + x = 150-9x

Now, as per the question, this number is 9 less than the original.

Equation:

(9x + 15) - 9 = 150 - 9x

= 9x + 15 - 9 = 150 - 9x

= 9x + 6 = 150 - 9x

= 9x + 9x = 150 - 6

= 18x = 144

$= x = \frac{144}{18}$

= x = 8

The number (By substituting the value of x) = 9(8) + 15

= 72 + 15 = 87

Therefore, the number is 87.