Question

the digits of a two digits number differ by 3 .if the digits are interchange, and the resulting number is added to the original number,w get 143 . what can be the original number​

Answer 1

Step-by-step explanation:

Let the digits be x&y

According to problem,

The difference of the digits.= 3

x - y = 3

x = 3 + y -----------------eqn(1)

Let the no.be 10x + y(general form of 2 digit number)

On inter changing the digits,the no.becomes 10y + x

If the original no.and interchanged no.are added,we get 143(given)

So,

10x + y + 10y + x = 143

11x + 11y = 143

On taking 11 as common,

11(x + y) = 143

x + y = 143/11

x + y = 13 ----------------eqn(2)

Substitute x = 3 + y in eqn(2)

(3 + y) + y = 13

2y + 3 = 13

2y = 13-3

2y = 10

y = 10/2

y = 5

Put y = 5 in eqn(1)

x = 3 + 5

x = 8

We assumed that number = 10x + y

So,

$number \: = \: 10(8) + 5$

$number = 80 + 5$

$number = 85$

HOPE IT HELPS...