Math, asked by nitin6351, 11 months ago

the numerator of a rational number is less than its denominator by 6 if one is added to both numerator and denominator the new number becomes 1/2 find the original number​

Answers

Answered by CᴀɴᴅʏCʀᴜsʜ
2

Answer:

Let the numerator be x

and the denominator be y

A/q

x - 6 = y

=> x = y + 6 .......(1)

Again,

(x+1 - 6)/(y + 1) = 1/2

=> (x - 5)/(y+1) = 1/2

=> 2x - 10 = y + 1

=> y = 2x - 10 -1

=> y = 2(y + 6) - 10 - 1 ....... {from (1)}

=> y = 2y + 12 - 11

=> y - 2y = 1

=> - y = 1

=> y = -1

Now

From eq. (1)

x = y + 6

x = -1 + 6

x = 5

Hence the fraction = x/y

= 5/-1

= -5/1

Therefore,

Numerator = -5

Denominator = 1

Answered by ItsMysteriousGirl
5

\huge\bf\underline{Question:}

The numerator of a rational number is less than its denominator by 6 if one is added to both numerator and denominator the new number becomes 1/2.Find the original number.

\huge\bf\underline{Solution:}

Let the denominator be x.Therefore,the numerator will be x-6.

Therefore the original fraction is \frac{ x  - 6}{x} .

According to the question the equation formed will be

\implies \frac{(x - 6) + 1}{x + 1}  =  \frac{1}{2}   \\  \\\implies \frac{x - 5}{x + 1}  =  \frac{1}{2} \\  by \:cross\: multiplication\\ \implies  2x - 10 = x + 1  \\  \implies \: x = 11

Original Fraction

 </u></strong><strong><u>\</u></strong><strong><u>i</u></strong><strong><u>m</u></strong><strong><u>p</u></strong><strong><u>l</u></strong><strong><u>i</u></strong><strong><u>e</u></strong><strong><u>s</u></strong><strong><u> </u></strong><strong><u>\frac{x - 6}{x} </u></strong><strong><u>\</u></strong><strong><u>\</u></strong><strong><u> </u></strong><strong><u>\</u></strong><strong><u>\</u></strong><strong><u> </u></strong><strong><u>\</u></strong><strong><u>i</u></strong><strong><u>m</u></strong><strong><u>p</u></strong><strong><u>l</u></strong><strong><u>i</u></strong><strong><u>e</u></strong><strong><u>s</u></strong><strong><u> </u></strong><strong><u>\frac{11 - 6}{11}</u></strong><strong><u>\</u></strong><strong><u>\</u></strong><strong><u> </u></strong><strong><u>\</u></strong><strong><u>\</u></strong><strong><u>\</u></strong><strong><u>i</u></strong><strong><u>m</u></strong><strong><u>p</u></strong><strong><u>l</u></strong><strong><u>i</u></strong><strong><u>e</u></strong><strong><u>s</u></strong><strong><u> </u></strong><strong><u>  \frac{5}{11}   \\

Therefore the original fraction is 5/11.

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