Question

A certain number between 10 and 100 is 8 times the sum of its digits. If 45 is subtracted from it the digits will be reversed. Find the number.


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Answer 1

Explanation:

let the digit in ten's place be x and unit place be y

given that 8*sum of digits = The original number

[ original number = 10*x + 1*y => 10x + y ]

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

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

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

also given that original number - 45 = new number

new number [ digits are reversed ie 10 y + x ]

10x + y - 45 = 10y + x

=> 9x - 9y = 45

=> x - y = 5 -------------------2

solving 1 and 2

x - y = 5 * 2

=> 2x - 2y = 10

[ add ]

- 2x + 7y = 0

_____________

0 + 5y = 10

______________

y = 2 and x = 7

therefore the number is 10x + y => 10*7 + 1*2

=> 72

Answer 2

Answer:

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Explanation:

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