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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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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 :

$\frac{10y+\hspace{0.17em}x}{10}=\frac{x+y}{4}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{{\displaystyle 10y+\hspace{0.17em}x}}{{\displaystyle 5}}=\frac{{\displaystyle x+y}}{{\displaystyle 2}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow 20y+\hspace{0.17em}2x=5x+5y\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow 15y=3x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{\Rightarrow}\mathbf{5}\mathbf{}\mathit{y}\mathbf{}\mathbf{=}\mathit{x}$

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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