A number consists of two digits whose sum is 9. If 27 is subtracted from the number its digits are reserved. Find the number.

# A number consists of two digits whose sum is 9. If 27 is subtracted from the number its digits are reserved. Find the number.

1. A
34
2. B
60
3. C
63
4. D
20

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### Solution:

Concept- Assuming two digits as $x$ and $y$. According to the conditions, we will solve the questions to find the number.
Number becomes $10x+y$
According to the condition,
$x+y=9$…………………………………(i)
Reversed form of the number,
$=10y+x$
Now, subtracting 27 from the given number and equating its reverse, we will get,
$⇒10x+y-27=10y+x$
$⇒10x+y-10y-x=27$
$⇒9x-9y=27$
$⇒9\left(x-y\right)=27$
$⇒x-y=3$………………………….(ii)
Adding equation (i) and (ii), we get
$⇒x+y+x-y=9+3$
$⇒2x=12$
$⇒x=6$
Putting the value of x in equation(i),
$⇒6+y=9$
$⇒y=3$
Therefore, number $=10x+y$
Number
Number
Hence, the correct answer is option 3.

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