A two-digit number is such that if a decimal point is placed between its digits, the resulting number is one-quarter of the sum of its digits. What is the original number? 
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Dear Student,

Please find below the solution to the asked query:

Let unit digit of given number =  x  and tens digit =  y  , So

Original number = 10 y + x 

And from given condition we get :

$$\begin{gathered} \frac{10 y +\hspace{0.17em}x}{10} = \frac{x + y}{4} \\ \Rightarrow \frac{{\displaystyle 10 y +\hspace{0.17em}x}}{{\displaystyle 5}} = \frac{{\displaystyle x + y}}{{\displaystyle 2}} \\ \Rightarrow 20 y +\hspace{0.17em}2 x = 5 x + 5 y \\ \Rightarrow 15 y =3 x \\ \mathbf{\Rightarrow }\mathbf{5}\mathbf{ }\mathit{y}\mathbf{ }\mathbf{=}\mathit{x} \end{gathered}$$
From above equation we can say that only at y  = 1 we get ' x ' as single digit number , so at y  =  1 we get from above equation :

5 ( 1 ) = x  ,

x  = 5 

Therefore,

Our original number = 10 ( 1 ) + 5 =  10 +  5 =  15                                            ( Ans )


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