Question

the digit if two number differ by 6.if the digits are interchange and the resulting no. is added to the original no. we get 132. what are original and new nos.

Answer 1

Step-by-step explanation:

Soln,

Let the no be 10x+y,

 Where,

  x = tens and y = ones

Now,

   x-y = 6

or, x = 6+y --- (i)

   10x+y+10y+x = 132

or, 11x+11y = 132

or, 11(x+y) = 132

or, x+y = 132/11

or, x = 12 - y ---(ii)

Comparing eqns (i) and (ii),

   6+y = 12-y

or, y+y = 12-6

or, 2y = 6

or, y = 6/2

or, y = 3

Putting the value of y in eqns (i),

   x = 6+y

or, x = 6+3

∴ x = 9

Finally,

∴The original no = 10x+y

                            = 10*9 + 3

                            = 90 + 3

                            = 93

∴The new no = 10y+x

                      = 10*3 + 9

                      = 30 + 9

                      = 39

Hope it was helpful.