Question

The sum of the digits of a two digits number is 12 The number obtained by interchanging the two digits exceeds to the given number by 18 .find the number.

Answer 1

Answer:

• The two-digit number is = 57

Given :

• The sum of the digits of a two digits number is 12.

• The number obtained by interchanging the two digits exceeds to the given number by 18.

To find :

• The new number =?

Step-by-step explanation:

Let the ones digit number of two digits of the number be x.

Then, the ten 's digit number of the two digit number be y.

Therefore, two-digit number is = 10x + y

And, the reversed number = 10y + x

According to the question :

x + y = 12

y = 12 – x ..... (1)

It is given that :

10y + x - 10x – y = 18

9y – 9x = 18

y – x = 2 ..... (2)

Substitute the value of y from eq (1) in eq. (2)

12 – x – x = 2

12 – 2x = 2

2x = 10

x = 5

Hence, x = 5

So, y = 12 – x = 12 – 5 = 7

Therefore, the two-digit number is = 57

Answer 2

Given:

• Sum of digits of two digit no. is 12
• no. obtained by interchanging two digits exceeds by 18.

To find :

The original number

Solution :

Let the tens digit of the required number be x and the units digit be y. Then,

X + y = 12.......... (1)

Required Number = (10x+y).

Required Number = (10x+y).Number obtained on reversing the digits = (10y+x).

Therefore,

= (10y+x)−(10x+y)=18

= 9y−9x=18

= y - x = 2.............. (2)

On adding both eq 1 and 2 we will get ,

2y = 14

y = 14/ 2

y = 7

Therefore, x = 5

Hence the required no. is 57.