Question

a number consists of two digits whose sum is 8 . if 18 is added to the number , its digits are interchanged. the number is??

Answer 1

Let the two digit no. be 10a + b. And,
a + b = 8.         -i
According to the question,
if 18 is added to the no. it's digits are interchanged.
∴(10a + b ) + 18 = 10b + a
⇒10a + b +18 = 10b + a
⇒10a - a + b - 10b = -18
⇒9a - 9b = -18
⇒9(a - b)= -18
⇒a - b = -2      -ii
In eqn. i,
a + b=8
or a = 8 - b 
Sustuting value of a in eqn. ii,
a - b = -2
⇒(8 - b) - b = -2
or 8 - 2b = -2
or -2b = -2 - 8
or - 2b = -10
or b = 5.
If b= 5, then a = 8 - b.
or a= 8 - 5
or a = 3.
∴ the no. 10a + b
                        =10*3 + 5
                        =30+5
                        =35.
Hence the no. is 35.