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

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

$\huge\bf\underline{Question:}$

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

$\implies \frac{x - 6}{x} \\ \\ \implies \frac{11 - 6}{11}\\ \\\implies \frac{5}{11} \\$

Therefore the original fraction is 5/11.

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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​

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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