Question

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

In answer key,it is coming 96.​

Answer 1

Let the digit in tens place be x,

and that in the unit place be y.

therefore, the no. will be 10x+y

Now, from 1st condition,

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

from 2nd condition,

10y + x = 10x + y - 27

: 10y - y + x - 10x = -27

: 9y - 9x = - 27

: 9 ( y - x ) = - 27

: -x + y = -27/9

: -x + y = - 3 .........( ll )

Add eqn l & ll

x + y = 15

+ -x + y = -3

____________

2y = 12

: y = 12/2

: y = 6

put y = 6 in eqn l.

i.e. x + y = 15

: x + 6 = 15

: x = 15 - 6

: x = 9

therefore, the 2 digit no. is 10x + y =

10 × 9 + 6 = 90 + 6

= 96

.......

.....