Question

A two – digit number is such that the ten’s digit exceeds twice the unit’s digit by 2 and the number obtained by interchanging the digits is 5 more than three times the sum of the digits. Find the two-digit number.
A.83
B.13
C.43
D.63

Answer 1

Hint: We can take two digits numbers as $ 10x+y $ where x= digit at ten’s place and y=digit at unit’s place and form the required equation from the above mentioned data. Inter-changing the digit means writing the number as $ 10y+x $ where y= digit at ten’s place and x= digit at unit’s place.

Complete step-by-step answer:
 In two digit number ten’s digit exceeds twice the unit’s digit by 2 , the number obtained by inter -changing the digits is 5 more than three times the sum of the digits
 Suppose the two-digit number is given by $ 10x+y $
Therefore, According to the question the relation between x and y
 $ x=2y+2 $ …………………( i )
After Inter-Changing
 $ 10y+x=3x+3y+5 $ …………………( ii )
Step 2: Simplifying equation ( ii ) we get,
 $ \begin{align}
& 10y+x=3x+3y+5 \\
& \Rightarrow 10y+x-3x-3y=5 \\
\end{align} $
 $ \Rightarrow 7y-2x=5 $ ………………..( iii )
Step 3: Putting equation ( i ) in equation ( iii ) we get,
 $ \begin{align}
& 7y-2(2y+2)=5 \\
& \Rightarrow 7y-4y-4=5 \\
& \Rightarrow 3y=9 \\
& \Rightarrow y=3 \\
\end{align} $
Step 3: Putting y=3 in equation ( i ) we get,
 $ \begin{align}
& x=2y+2 \\
& \Rightarrow 2\times 3+2 \\
& \Rightarrow \,x=8 \\
\end{align} $
So, the digit formed is,
 $ 10x+y=10(8)+3=83 $
Hence the required two digits number is 83.

So, the correct answer is “Option A”.

Note: In this type of question students always get confused about how to take two digits number and the second confusion that arises is to write the place value of 2 digit number.So take care of these two things.