Question

the sum of the digits of two digit number is 12 if the new number formed by reversing the digits is greater than the original number by 18 then find the original number

Answer 1

Answer:

57

Step-by-step explanation:

Let the 2 digit number be xy

We have:

x+y=12 ---> (1)

yx- xy=18 ---> (2)

We can write the second equation as:

10y+x-(10x+y)=18

And simplify:

9y-9x=18

y-x=2

y=x+2

Considering this in equation 1 we get:

x+y=12

x+x+2=12

2x=10

x=5

So knowing the value of x, we find the value of y:

y=x+2=5+2=7

We have the 2 digit number of 57

Its sum of digits=12

Reverse =75

The difference with its reverse=75-57=18

Answer 2

Here is the answer!!

Hope it helps....

Let,

Tens digit = x

Ones digit = y

Therefore,

No. formed = 10x + y

No. obtained by reversing

the digits = 10y + x

ATQ.

x + y = 12 ----------- 1

And

10y + x = 18 + 10x + y

10x - x - 10y + y + 18 = 0

9x - 9y = -18

x - y = -2 -----------2

Adding 1 and 2

x + y + x - y = 12 + ( - 2)

2x = 12 - 2

2x = 10

x = 10/2

x = 5 ---------- 3

i.e. tens digit = 5

Using 3 in 1

5 + y = 12

y = 12 - 5

y = 7

i.e. ones digit = 7

Thus,

No. obtained = 57