Question

A 2 digit number is 3 times the sum of digit.if 45 is added to the number, it's digits are interchanged. the sum of digit of the number is

Answer 1

let the digit at unit place be x
and at ten place be y
so the no =10x+y
on inter changing the digits
New no=10y+x

ATQ
2 digit number is 3 times the sum of digit.

=>. 10x+y=3(x+y)
=>. 10x+y=3x+3y
=>. 10x-3x+y-3y=0
=>. 7x-2y=0....................(1)

45 is added to the number, it's digits are interchanged
=>. 10x+y+45=10y+x
=>. 10x-x+y-10y=-45
=>. 9x-9y=-45
=>. 9(x-y)=-45
=>. x-y=-5.....................(2)

Solving (1). &. (2) for x and y
7x-2y=0
2x-2y= -10
=>5x=10......(on subtracting)
=>. x=2
Putting the value of x in (2) we get
2-y= -5
=> y=7

So the no is 27
sum of the digits=9