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

Hello...

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

Lets assume unit digit be = x
And assume Tenth digit be = y

So,

=> The number = 10y + x

Given:-
=> x + y = 9
x = 9 - y ........ (1)

=> 10y + x = 6x
10y = 6x-x
10y = 5x
y = 5x / 10 ......... (2)

=> Substituting (1) in (2)
y = 5 ( 9 - y) / 10
y = 45 - 5y / 10
10y = 45 - 5y
10y + 5y = 45
15y = 45
y = 45/15
y = 3
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So,
x = 9 - y
x = 9 - 3
x = 6
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=> Therefore,

Number = 10y + x
= 10 ( 3 ) + 6
= 30 + 6
= 36
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So the required number is 36

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