Question 1207157
A two digit number is such that the sum of the digits is 12 if the digits are interchanged the value of the new number formed is15 more than twice the value of the original number find the original number

Let ten's digit be x
and the units digit be y

the sum of the digits is 12
x+y=12..............................1

if the digits are interchanged the value of the new number formed is15 more than twice the value of the original number
Value of original number = 10x+Y

Reverse number will be 10y+x

10y+x = 15+2(10x+y)


10y+x = 15+20x+2y

rearrange

10y-2y +x-20x = 15

8y-19x  = 15.......................2

solve 1 & 2

Multiply (1) by -8

-8x-8y= -96..................3
add (1) &(3)
-27x = -81

x = 3

now x+y =12

so y = 12-3 = 9

So the number is 39

check


93 = 15+2(39)

93 = 15+ 78=93

LHS = RHS