Question

a two digit number is 4 times the sum of its digit. if 8 is added to the number the digit gets reversed. find the number ?​

Answer 1

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Let the digits be x and y

Then the two-digit number is 10x + y

Given that: 10x + y = 4 (x + y) 

       10x + y = 4x + 4y

        6x = 3y

          y = 2x  --------------- 1

And 10x + y + 18 = 10y + x

Or           9y – 9x =

18 ---------------- 2

Substitute the value of y in eqn 2

18x – 9x = 18

9x = 18

x = 2

Therefore  y = 2x =

2*2 = 4

And the number is 10x + y = 10*2 + 4 = 24

Answer: The two-digit number is 24.

$\bf\underline{By-Saksham }$

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Answer 2

Let the two digit number be 10x + y. 10x + y = 4(x + y) + 3 6x - 3y = 3 2x - y = 1 ..........(i) 10x + y + 18 = 10y + x 9x - 9y = - 18 x - y = - 2 ......(ii) from (i) and (ii), we get so, x = 3 and y = 5 so, the number = 35