Math, asked by binalprajapati1984ra, 6 months ago

If (p)/(q)=4.bar(23) and (x)/(y)=0.bar(67) where p q and x y are co- prime integers and q y!=0 then (py)/(qx) equals
can anybody answe thid in 5 min​

Answers

Answered by pulakmath007
25

\displaystyle\huge\red{\underline{\underline{Solution}}}

GIVEN

 \displaystyle \sf{ \frac{p}{q}  = 4. \overline{23} \:  \:  \: and \:  \:  \:  \frac{x}{y}  = 0. \overline{23} \:  \: }

where p q and x y are co- prime integers

TO DETERMINE

 \displaystyle \sf{ \frac{py}{qx}   \: }

CALCULATION

Let

 \displaystyle \sf{ k= 4. \overline{23} \:  }

 \implies \:  \displaystyle \sf{ k= 4. 232323........ \:  \:  \:  \:  \:  \: (1)\:  }

Multiplying both sides by 100 we get

 \displaystyle \sf{ 100k= 423. 232323........ \:  \:  \:  \:  \:  \: (2)\:  }

Equation (2) - Equation (1) produce

 \displaystyle \sf{ 99k= 419  }

  \implies\displaystyle \sf{k=  \frac{419}{99}   }

Therefore

 \displaystyle \sf{  \frac{p}{q} =  4. \overline{23} \:  =  \frac{419}{99}  } \:  \:  \:  \: ....(3)

Similarly

 \displaystyle \sf{ \frac{x}{y} =   0. \overline{67} \:  =  \frac{67}{99}  }

  \implies \: \displaystyle \sf{ \frac{y}{x} =\frac{99}{67}  } \:  \:   \:  \:  \: \: ....(4)

Now Equation (3) × Equation (4) gives

 \displaystyle \sf{ \frac{py}{qx}  =  \frac{419}{99}    \times  \frac{99}{67} \: }

 \implies \:  \displaystyle \sf{ \frac{py}{qx}  =  \frac{419}{67}    \: }

RESULT

 \boxed{ \:  \displaystyle \sf{ \:  \:  \:  \:  \frac{py}{qx}  =  \frac{419}{67}    \: } \:  \: }

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