Question

a two digit number is three times the sum of its digits.if 45 is added to it the digits are reversed.the number is

Answer 1

Let the no. be 10x + y
Sum of its digits = x+y

According to question

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

Now,

10x + y + 45 = 10y + x
=> 9x - 9y = - 45
=> x - y = - 5
=> x= y-5 - - - - - - - - - - - - - (2)

On putting the value of x in equation (1),we get
7(y-5) - 2y = 0
=> 7y - 35 - 2y = 0
=> 5y = 35
=> y = 7

x= y-5
=> x= 2

No. = 27

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Answer 2

original no:
ones digit=y
tens digit=x
the original no:10x+y
reversed no:10y+x

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

10x+y+45=10y+x
9x+45-9y=0
x-y=-5 ----eq.2

from eq.1 and eq.2
x=2 and y=7
therefore the no. is 
27