Question

a number counting of 2 digit whom sum is 8 if 18 is added to the numbers it is digit are received find the number​

Answer 1

GIVEN

A two digit number = xy

x + y = 8

we can write that two digit number xy as

xy = 10x + y

If 18 is added the number get reversed.

TO FIND :- Those numbers

SOLUTION

10x + y + 18 = 10y + x

=> 9x - 9y + 18 = 0

=> 9x - 9y = - 18

=> 9(y - x) = 18

=> y - x = 2 ... eq.01

Also given that x + y = 8 ...eq.02

Solving the system of equation by elimination method :-

Adding eq.01 and 02 we get,

x + y + y - x = 2 + 8

=> 2y = 10

=> y = 5

Substituting the value at equation 02 we get

x + 5 = 8

=> x = 3

Verification :-

Substituting both values in LHS of eq.01

LHS= y - x = 5 - 3 = 2 = RHS

As LHS = RHS, Our solution is correct.

Hence the number is 35 . (ANS)

NOTE

When 18 is added to 35 we get 53 which is just reversing the digits.

Answer 2

SOLUTION:-

Given:

•A number counting of 2 digit whom sum is 8.

•If 18 is added to the number it's digit are reserved.

To find:

The number.

Explanation:

Let the number be RM.

Two Digit number whom sum is 8.

R + M= 8

R= 8 -M............(1)

Let Original number is 10M + R

Let reversed number is 10R + M.

According to the question:

18 number is added to reversed number, we get;

=) 10R +M +18 = 10M +R

=) 10R -R +M -10M+18=0

=) 9R -9M = -18

=) R - M = -2..............(2)

Putting the value of R in equation (2), we get;

=) 8 - M -M= -2

=) 8 -2M = -2

=) -2M = -2 -8

=) -2M = -10

=) M= -10/-2

=) M= 5

Now,

Putting the value of M in equation (1), we get;

R= 8- 5

R= 3

Thus,

The number is RM=35.