Question

the sum of the digits of a two dgit no. is 7 if the no. formed by interchanging the digits is less than the original no. by 27 then the original no. is?

Answer 1

The Original number is 52

Step-by-step explanation:

Let the two digits be x and y

The , The sum of the two Digits is 7

So

x +y = 7

x = 7-y-------------------------------(1)

The original number is
`x * 10 +y`---------------(2)

Now if we interchange the digits

The interchanged number will be
`y * 10 + x`---------(3)

Interchanged = Original – 27

`y * 10 + x = x * 10 + y -27`

`10y + x =10x + y -27`

Group the like terms

`10y -y =10x -x -27`

`9y = 9x -27`--------------------------(4)

Substituting (1) in(4)

`9y = 9(7-y) -27`

`9y = 63 -9y -27`

`9y+9y = 63-27`

`18 y = 36`

`y =(36)/(18)`

y = 2-------------------------------------(5)

Substituting (5) in(1)

x = 7 -y

x =7-2

x =5

Now From eq(1)

The original number will be

=10x +y

= 10(5) +2

= 50 +2

=52