Question

The numerator and denominator of a rational number are in the ratio 3:46
denominator is increased by 3. the ratio becomes 3:5. Find the rational number
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Answer 1

$\large{\underline{\purple{\mathfrak{Given - }}}}$

• Numerator and denominator of a rational number are in the ratio 3 : 4
• Denominator is increased by 3.
• New ratio becomes 3 : 5

$\large{\underline{\purple{\mathfrak{To \: Find - }}}}$

• That rational number.

☯︎ $\large{\underline{{\mathfrak{Put \: k \: in \: the \: ratio \: - }}}}$

• Numerator ➝ 3k
• Denominator ➝ 4k

Denominator increased by 3 ➝ 4k + 3

$\sf\implies \: new \: fraction \: = \frac{3k}{4k + 3}$

__________________

★ $\large{\underline{\pink{\mathfrak{According \: to \: the \: question - }}}}$

$\sf\implies \: \frac{3k}{4k + 3} = \frac{3}{5} \\ \\ \sf\implies3k \times 5 = 3(4k + 3) \\ \\ \sf\implies \: 15k = 12k + 9 \\ \\ \sf\implies \: 15k - 12k = 9 \\ \\ \sf\implies \: 3k = 9 \\ \\ \sf\implies \: k = \cancel \dfrac{9}{3} \\ \\ \sf\implies \: k = 3$

$\large{\underline{\blue{\mathfrak{Put \: the \: value \: of \: k \: in \: the \: ratio \: - }}}}$

• Numerator ➝ 3(3) ➝ 9
• Denominator ➝ 3(4) ➝ 12

$\sf\therefore$ The rational number is $\dfrac{9}{12}$