Question

the sum of 2 digit no. is 9. Also 9 times this no. is twice the no. obtained by reversing the order of digits. Find the number

Answer 1

Let digit at unit place=x
Let digit at tens place = y
Actual No. = 10x+y
Reversing no.=10y+x
A.T.Q
x+y=9.....(1)
9(10x+y)=2(10y+x)
90x+9y=20y+2x
88x=11y
8x=y.....(2)
Put eq.(2) in (1)
x+8x=9
9x=9
x=1
Hence from 1
y=8

Check:We have been said that sum of two digit no. is 9 hence from answer we received
x+y=9
9=9
L.H.S=R.H.S
Hence proved