Linear Equation 15

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The sum of the digits of a two digit number is 9. If the number is divided by its unit's digit, the quotient is 6.
Find the number.

Solution:

Let the unit's digit = x

=> the ten's digit = 9 - x

And, the number = 10 (9 - x) + x = 90 - 10 x + x = 90 - 9 x

Given, (90 - 9 x) / x = 6

=> 90 - 9 x = 6 x

i.e. 90 = 6 x + 9 x

=>15 x = 90

and, x = 90 / 15 = 6

Therefore, the required two digit number = 10 (9 - x) + x = 10 (9 - 6) + 6 = 36

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