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

Original fraction = ⁴/₇

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 (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 (2x)/(x+3+14)=(2)/(3)\left((x)/(x+3)\right)`

`\implies (2x)/(x+17)=(2x)/(3(x+3))`

`\implies (2x)/(x+17)=(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 (4)/(4+3)=(4)/(7)`

Therefore, the original fraction is ⁴/₇.

Answer 2

• The original fraction is 4/7

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