1.

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

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let the ten's digit be x and unit digit be y.

ATQ,

=> 8(x + y) = 10x + y

=> 8x + 8y = 10x + y

=> 2x - 7y = 0 ------(1)

Also

=> 10x + y - 45 = 10y + x

=> 9x - 9y = 45

=> (x - y = 5)------(2)

Subtract (2) from (1)

=> 2x - 7y - (2x - 2y) = -10

=> -5y = -10

=> y = 2

Thus x - 2 = 5

=> x = 7

Thus ORIGINAL number = 70 + 2 = 72

Hope this helps you again


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