Question

The sum of the digit of a two digit number is 9 the
number is 6 times the unit digit . Find the number

Answer 1

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Here is your answer...
Let t = the tens digit, u = the unitis digit, t + u = 9
Solve t by adding -u to each side.
t = 9 - u
value of number is 10t + u.
(10t + u) = 6u
Substitute (9 - u) for t 
10(9 - u) + u = 6u
90 - 10u + u = 6u
90 - 9u = 6u
add 9u 
90 = 15u
divide side by 15
6 = u
t+u = 9
t + 6 = 9
add -6 
t = 3
t+u = 9, 3+u = 9 and u = 6
number is 36

Answer 2

Let the tens place digit be a

And Unit place digit be b

First condition,

a+b = 9

a = 9-b -------(1)

Second condition,

6* b = 10a + b

=> 6b = 10 (9-b) + b , (using equation 1)

=> 6b = 90 - 10b + b

=> 6b = 90-9b

=> 15b = 90

=> b = 6

On putting the value of b in equation 1, we get

a= 9 - 6

a= 3

Number = 10 a + b

= 36