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

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answer is C.

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Detailed Solution

Concept- Assuming two digits as

x

and

y

. According to the conditions, we will solve the questions to find the number.
Number becomes

10 x + y

According to the condition,

x + y = 9

…………………………………(i)
Reversed form of the number,

= 10 y + x

Now, subtracting 27 from the given number and equating its reverse, we will get,

\Rightarrow 10 x + y - 27 = 10 y + x

\Rightarrow 10 x + y - 10 y - x = 27

\Rightarrow 9 x - 9 y = 27

\Rightarrow 9 (x - y) = 27

\Rightarrow x - y = 3

………………………….(ii)
Adding equation (i) and (ii), we get

\Rightarrow x + y + x - y = 9 + 3

\Rightarrow 2 x = 12

\Rightarrow x = 6

Putting the value of x in equation(i),

\Rightarrow 6 + y = 9

\Rightarrow y = 3

Therefore, number

= 10 x + y

Number

= 10 \times 6 + 3

Number

= 63

Hence, the correct answer is option 3.

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