A certain number between 10 and 100 is 8 times the sum of its digits, and if 45 be subtracted from it the digits will be reversed. Find the number.
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Answer:let the number be xy
value of number = 10x+y
10x+y = 8(x+y)
10x+y =8x+8y
2x-7y=0....................(1)
10x+y-45 = 10y+x
9x-9y=45
x-y = 5.................(2)
multiply by -2
-2x+2y=-10
add to (1)
-5y=-10
y=2
x-y =5
x=7
Number = 72
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