Question

The numerator and denominatorof a rational numberare in the ratio3:4if the denominator is increasedby 3 the ratiobecome 3:5find the rational number

Answer 1

Let the numerator be x and denominator be y.

Condition 1

The numerator and denominator of the rational number are in the ratio 3:4.

Hence,

$\rm \dfrac{x}{y}=\dfrac{3}{4} \\ \\ \bf \bullet\qquad 4x = 3y \qquad\qquad ...[1]$

Condition 2

If the denominator is increased by 3 the ratio becomes 3:5.

Hence,

$\rm \dfrac{x}{y+3}=\dfrac{3}{5}$

$\rm \dashrightarrow 3(y+3)=5(x)$

$\bf\bullet\qquad 3y+9=5x \qquad\qquad ...[2]$

★Solution

Substituting the value of 3y from [1] in [2]

→ 3y + 9=5x

→ 4x + 9 = 5x

→ 9 = 5x - 4x

→ x = 9 ...[3]

Substituting the value of x from [3] in [1]

→ 4x = 3y

→ 4(9) = 3y

→ 36 = 3y

→ y = $\dfrac{36}{3}$

→ y = 12

Original rational number

$\dashrightarrow\rm \dfrac{x}{y}=\bf\dfrac{9}{12}$