Question

The sum of the 2 digit no. Is 9. Also, nine times this no. Is twice the no. Obtained by reversing the order of the digit. Find the no.

Answer 1

let the didit at tens place be a and at units place be b.

by the condition:a+b=9

i.e. a=9-b. .........................(1)

therefore, the no. is 10a+b........(2)

reverse of this no. is 10b+a.

By the condition:9(10a+b)=2(10b+a)

90a+9b=20b+2a

90a-2a=20b-9b

88a=11b

88a-11b=0

88(9-b)-11b=0. .......from(1)

792-88b-11b=0

792-99b=0

792=99b

b=792/99=8. ..........(3)

Put (3) in (1)

a=9-8

a=1

from (2)

10(1)+8=10+8=18

Therefore the no. is 18