1.

The sum of a two–digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?

Answer» let tens digite of number is`x`
let unit digit be`y`
number= `(10x+y)`
if no is reversed then
unit digit `x` & tens digit `y`
reversed number= `(10y+x)`
acc to question
`(10x+y) + (10y+x)= 66`
`11x+11y=66`
so, `x+y=6`
now `x-y=2`
or `y-x=2`
case-1 `x-y=2 & x+y=6`
by adding both, we get`2x= 8`
`x=4`
`y=2`
so number will be `4*10=2 = 42`
case 2 : `y-x=2 & x+y=6`
by adding both, we get `2y= 8`
`y=4`
`x=2`
now number will be `24`
answer is 24 and 42


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