Question

A certain no. Between 10 and 100 is 8 times the sum of digits and if 45 be subtracted from it the digits will be reversed find the no.

Answer 1

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Let the number be 10a + b

Given,

10a + b = 8 ( a + b )

10a - 8a + b - 8b = 0

2a - 7b = 0

2a = 7b

Also, 10a + b - 45 = 10b + a

9a - 9b = 45

9 ( 7 b / 2 ) - 9b = 45

(7b / 2) - b = 5

7b - 2b / 2 = 5

5b / 2 = 5

b = 2

2a = 7 ( 2 )

a = 7

So, Number = 72

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Answer 2

Let the number be 10a + b

Given,

10a + b = 8 ( a + b )

10a - 8a + b - 8b = 0

2a - 7b = 0

2a = 7b

Also, 10a + b - 45 = 10b + a

9a - 9b = 45

9 ( 7 b / 2 ) - 9b = 45

(7b / 2) - b = 5

7b - 2b / 2 = 5

5b / 2 = 5

b = 2

2a = 7 ( 2 )

a = 7

So, Number = 72