Question

A certain number between 10 and 100 is 8 times the sum of its digits and if 45 be subtracted from it the digits get reversed. find the number

Answer 1

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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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