Question

the numerator and the denominator of a rational number are in the ratio of 3:4 if the denominator is increased by three the ratio is 3:4 find the rational number​

Answer 1

Given data : The numerator and the denominator of a rational number are in the ratio of 3:4. If the denominator is increased by three the ratio is 3:4.

To find : The rational number ?

Solution : Let, numerator's term be 3x and denominator's term be 4x.

⟹ numerator/denominator = 3x/4x

Now according to given : If the denominator is increased by three the ratio is 3:4.

⟹ 3x/{4x + 3} = 3/4

⟹ 4 * 3x = 3 * {4x + 3}

⟹ 12x = 12x + 9

⟹ 12x - 12x = 9

⟹ 0 ≠ 9

Here we are not getting output.

{Here some correction in question}

Given data : The numerator and the denominator of a rational number are in the ratio of 3:4. If the denominator is increased by three the ratio is 3:5.

To find : The rational number ?

Solution : Let, numerator's term be 3x and denominator's term be 4x.

⟹ numerator/denominator = 3x/4x ____( 1 )

Now according to given : If the denominator is increased by three the ratio is 3:5

⟹ 3x/{4x + 3} = 3/5

⟹ 5 * 3x = 3 * {4x + 3}

⟹ 15x = 12x + 9

⟹ 15x - 12x = 9

⟹ 3x = 9

⟹ x = 9/3

⟹ x = 3

Put value of x in eq. ( 1 )

⟹ numerator/denominator = 3x/4x

⟹ numerator/denominator = {3 * 3}/{4 *3}

⟹ numerator/denominator = 9/12 or 3/4

Answer : Hence fraction is 9/12 (or 3/4) and If the denominator is increased by three then fraction become 9/15 (or 3/5).