Question

The sum of the numerator and the denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduce to 1/3 . find the fraction

Answer 1

Let us assume, x and y are the numerator and denominator of a fraction x/y

Given:

x + y = 18 --------------1

Also given:

x / (y + 2) = 1/3

3x = y + 2

3x – y = 2 ------------------2

Multiply equation 1 by 3

3x + 3y = 54 ----------------3

Subtract eqn 2 from eqn 3

4y = 52

y = 13

Therefore, x = 18 – y = 12 – 13 = 5

Therefore, original fraction = x/y = 5/13

Answer 2

Aɴꜱᴡᴇʀ

☞ Your answer is $\sf\frac{5}{13}$

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Gɪᴠᴇɴ

➳ The sum of numerator and denominator of a fraction is 18.

➳ If the denominator increased by 2 the fraction reduces to 1/3.

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Tᴏ ꜰɪɴᴅ

➢ The original fraction?

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Sᴛᴇᴘꜱ

Let the numerator and denominator of the fraction be x and y respectively.

$\underline{\boxed{\green{\sf Original \: fraction = \dfrac{x}{y}}}}$

As per the Question,

❍ The sum of numerator and denominator of the fraction is 18.

$\implies \sf x + y = 18 \\\\\implies \sf x = 18 - y \: \: \: \dots (i)$

Also,

✭ If the denominator increased by 2 the fraction reduces to 1/3.

❍ Equation :

$\leadsto \sf \frac{x}{y+2} = \frac{1}{3} \\\\\leadsto \sf 3x = y + 2 \\\\\leadsto \sf 3(18-y) = y + 2$

[ Using equation (i) ]

$\sf \dashrightarrow 54 - 3y = y + 2\\\\\dashrightarrow \sf - 3y - y = 2 - 54 \\\\\dashrightarrow\sf - 4y = - 52 \\\\\dashrightarrow \sf y = \frac{-52}{-4} \\\\\dashrightarrow\red{ \sf y = 13}$

Now, substituting the value of y in (i),

$\sf \dashrightarrow x = 18 - y \\\\\dashrightarrow \sf x = 18 - 13 \\\\\dashrightarrow \red{\sf x = 5}$

Thus, original fraction =$\sf \dfrac{x}{y}$

$\pink{ \sf \longrightarrow\dfrac{5}{13} }$

Hence, the original fraction is 5/13.

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