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# Sum of the digits of a two digit no. is 9. when we interchange the digit it is found that the resulting new no. is greater than the orignal no. by 27. What is the two digit no. is?

Ankit Jaiswal
165 Points
5 years ago
Let the 2 digit number as
10b + a
so here the digit at tens place is b and at units plac a
it is given that
a + b = 9..........................(eq 1)
and
10b + a = 10a + b + 27
$\therefore$ 9b – 9a = 27
$\therefore$ 9( a - b ) = 27
$\therefore$ a – b = 3.........................(eq 2)
now on adding eq1 and eq2
we get
a + b + a - b =3+9
$\therefore$ 2a = 12
$\therefore$ a = 6
now on substituting the value of a in eq2
a – b = 3
$\therefore$ 6 – b= 3
$\therefore$ b = 6 – 3 = 3
therefore the number is
10b + a = 30 + 6 = 36