Question

The sum of a digits of a 2 digit number is 15. If the number formed by reversing the digits is less than the original number by 27, find the original number.

Answer 1

Answer:

Step-by-step explanation:

10x+y original

10y+x reversed

10y+x = 10x + y -27

9y -9x = -27

y -x = -3

y + x = 15

2y = 12 so y = 6

x = 9

number = 96

Answer 2

$\textbf{\huge{ANSWER:}}$

$\sf{Given:}$

x + y = 15 ....(1)

R.N. = O.N. - 27

R.N. -》 Reversed Number
O.N. -》 Original Number

Original Number = 10x + y

Reversed Number = 10y + x

Then according to the given information :-

=》 10y + x = 10x + y - 27

By simplifying (1), we get :-

y = 15 - x

Put the value obtained by simplifying (1) into the previous equation :-

=》 10y + x = 10x + y - 27

Put the value and solve

=》 10 ( 15 - x ) + x = 10x + 15 - x - 27

Now solve it further

=》 150 - 10x + x = 9x - 12

Some more steps

=》 150 + 12 = 9x + 10x - x

Last step

=》 162 = 18x

Take it to L.H.S. and solve

=》 $x = \frac{162}{18}$

Divide and Get the final value

=》 $\tt{x = 9}$

Put the value of x in (1) and Get the value of y :-

y = 15 - 9

=》 6

We before found that :-

Original Number = 10x + y

=》 10 × 9 + 6

=》 90 + 6

=》 $\sf{96}$

There's your answer!