Question

The denominator of a fraction exceeds numerator by 3. If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction.

Answer 1

Answer:

Original fraction = ⁴/₇

Step-by-step explanation:

Numerator:  top of the fraction

Denominator: bottom of a fraction

Let x be the original numerator.

If the denominator of a fraction exceeds the numerator by 3:

$\implies \dfrac{x}{x+3}$

If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:

$\implies \dfrac{2x}{x+3+14}=\dfrac{2}{3}\left(\dfrac{x}{x+3}\right)$

$\implies \dfrac{2x}{x+17}=\dfrac{2x}{3(x+3)}$

$\implies \dfrac{2x}{x+17}=\dfrac{2x}{3x+9}$

Cross multiply:

$\implies 2x(3x+9)=2x(x+17)$

Divide both sides by 2x:

$\implies 3x+9=x+17$

Subtract x from both sides:

$\implies 2x+9=17$

Subtract 9 from both sides:

$\implies 2x=8$

Divide both sides by 2:

$\implies x=4$

Substitute the found value of x into the original fraction:

$\implies \dfrac{4}{4+3}=\dfrac{4}{7}$

Therefore, the original fraction is ⁴/₇.

Answer 2

Answer:

• The original fraction is 4/7

Step-by-step explanation:

Let the fraction be x/y.

According to question we have the following equations.

The denominator of a fraction exceeds numerator by 3:

• y = x + 3

If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:

• 2x/(y + 14) = (2/3)*(x/y)

Change the fraction as below and solve for y:

• 2x /(y + 14) = 2x/(3y)                       Nominators are same
• y + 14 = 3y                                      Compare denominators
• 2y =  14
• y = 7

Find the value of x using the first equation:

• 7 = x + 3
• x = 7 - 3
• x = 4

The fraction is:

• x/y = 4/7