Question

The digit at the tens place is 5 less than twice the digit at units place. The sum of original number and the number obtained by interchanging the digits is 176. Find the two digit number.

Answer 1

Number is 62.

Let say ‘x' is digit on one's place so 3x is digit on tens' place

So number is 10*3x+x=31x

Now if reverse the possition of digit new number is

10*x+3x=13x

As given new number is less by 36 from old number

31x-36=13x

18x=36

x=2

So number is 10*3*2+2=62.

Answer 2

Let ones place digit be x

Let tens place digit be y

Given tens place is 2x-5

Therefore y=(2x-5)

10y=(2x-5)10

Number is 10(2x-5)+x

=20x-50+x

=21x-50 eq...1

When digits are interchanged

x will be on tens place (therefore 10x)

And y( ie 2x-5) will be on ones place

Number formed will be

10x+2x-5

12x-5 eq...2

Add eq...1 and 2

(21x-50)+(12x-5)=176

33x-55=176

33x=176+55

33x=231

x=7

10y=(2x-5)10

(2(7)-5)10

(14-5)10

(9)10

90

Number is 10y+x

90+7=97