Question

a two digit number is obtained by either multiplying sum of the digits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding 2 . Find the numbers.

Answer 1

hi payal ,

Let the two digit number be 10x+y
A two digit number is obtained by

multiplying sum of the digits by 8 and adding 1
10x+y = (x+y)8 + 1
10x+y = 8x + 8y + 1
2x = 7y + 1
x= 3.5y +0.5

or by multiplying the difference of the digits by 13 and adding 2
10x+y = (x-y)13 + 2
10x+y = 13x - 13y + 2
3x = 14y - 2

substituting x value in above equation
3(3.5y + 0.5) = 14y -2
10.5y + 1.5 = 14y -2
3.5y = 3.5
y = 1

so
x = 3.5y + 0.5 = 3.5 + 0.5 = 4

hence the required two digit number is 10x+y = 40+1 = 41

Hope it helped.
Let me know if any doubts.
Cheers !!!