Question

The sum of digits of a 2-digit number is 11. If the number is less than the number obtained by interchanging the digits by 9 , find the number.

Answer 1

a+b=11
Original no.=10a+b
the no. formed by interchanging its digit=10b+a
=(10b+a)-(10a+b)
=10b+a-10a-b
=9b-9a=9
=b-a=1
Now,by subtracting b-a=1 from a+b=11
we get=2a=10
a= 5
Then, Since its given that:-
a+b=11
so,
5+b=11
b=11-5
b=6
Hence, the original no. =56(Answer)

Answer 2

let the number be 10x+y

given,
x+y=11. ....... eqn.1

10x+y=10y+x -9

9x -9y= -9. ......eqn.2
from eqn.1
9x+9y =99. ......... eqn.3


solving eqn.2 and eqn.3 , we get
18x=90
=> x=90/18
=>x=5
=>from eqn.1

x+y=11
=>y=11-x
=> y=11-5
=>y= 6
.therefore the num is
10x+y
=>50+6
=>56
the num is 56