Question

the numerator and denominator of a rational number are in the ratio 3:4. If the numerator is decreased by 3, the ratio becomes 3:5.find the rational number.​

Answer 1

Given: The Numerator and Denominator are in the ratio of 3:4.

Therefore,

❏ Let the numerator be 3x and Denominator be 4x.

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$\underline{\boldsymbol{According\: to \:the\: Question :}}$

⠀

• If the numerator is decreased by 3, the ratio becomes 3:5.

⠀

$:\implies\sf \dfrac{3x - 3}{4x} = \dfrac{3}{5} \\\\\\:\implies\sf 5 \Big(3x - 3 \Big) = 3 \Big(4x \Big) \\\\\\:\implies\sf 15x - 15 = 12x \\\\\\:\implies\sf 3x = 15\\\\\\:\implies\sf x = \cancel\dfrac{15}{3}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 5}}}}}\:\bigstar$

⠀

Hence,

⠀

• Numerator, 3x = 3(5) = 15
• Denominator, 4x = 4(5) = 20

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$\therefore\:{\underline{\sf{Hence, \: required\: rational \: number \ is\: \bf{\dfrac{15}{20}}}}}$

Answer 2

Gɪᴠᴇɴ :

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

Lᴇᴛ,

• Numerator be 3x.

• And denominator is 4x.

Tᴏ Fɪɴᴅ :

• The rational fraction.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

➣ If numerator is decreased by 3, then the new numerator is

$:\longrightarrow\:\:\bf{3x\:-\:3}$

Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ,

➣ If 3 is decreased from the numerator, then the ratio becomes 3 : 5.

$:\implies\:\:\bf{\dfrac{3x\:-\:3}{4x}\:=\:\dfrac{3}{5}}$

$:\implies\:\:\bf{5\times{(3x\:-\:3)}\:=\:3\times{4x}}$

$:\implies\:\:\bf{15x\:-\:15\:=\:12x}$

$:\implies\:\:\bf{15x\:-\:12x\:=\:15}$

$:\implies\:\:\bf{3x~=~15}$

$:\implies\:\:\bf{x\:=\:\dfrac{15}{3}}$

$:\implies\:\:\bf\pink{x\:=\:5}$

Hᴇɴᴄᴇ,

➛ Numerator = 3x = 3 × 5 = 15

➛ Denominator = 4x = 4 × 5 = 20

$\\ \Large\bf\orange{Therefore,}$

The rational fraction is $\bf{\dfrac{15}{20}}$.