want to verify my answer

Asked by shobhitdc | 28th May, 2010, 11:10: AM

Expert Answer:

Dear Student,

 

Let the digit at one's place is y and the digit at ten's place is x

So the two digit number is 10x + y

And the number formed by reversing the digits is 10y + x

According to the statement,

(10x + y) + (10y + x) = 132

i.e.              11x + 11y = 132

or                  x + y = 12   ……………………….(i)

 

Also, when 12 is added to the original number it becomes 5 times (x + y)

i.e.                     12 + 10x + y = 5(x + y)

or                      12 + 10x + y – 5x – 5y = 0

or                      5x – 4y = – 12   …………………….(ii)

 

Equations (i) and (ii) represent a system of linear equations in two variables.

Now, we solve the two equations for x and y

{4 × equation (i)} + equation (ii) gives

    4x + 4y + 5x – 4y = 48 – 12

i.e.            9x = 36

or               x = 4

Substituting this value of x in (i), we get

4 + y = 12

Which means     y = 12 – 4

                   So,   y = 8

Thus we have found that x = 4 and y = 8

Hence, the two digit number is

10 × 4 + 8  =   48

 

Regards,

Team

Topper Learning

Answered by  | 28th May, 2010, 11:42: AM

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