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.

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Answer 1

Let the numerator & denominator be 3x and 4x

Numerator is decreased by 3

According To The Question

3x/4x - 3 = 3/5

Applying Cross Multiplication

( 3x - 3 )5 = 3( 4x )

15x - 15 = 12x

Transporting 12x to LHS And -15 to RHS, we get

15x - 12x = 15

3x = 15

x = 15/3

x = 5

Numerator = 3 × 5 = 15

Denominator = 4 × 5 = 20

Therefore, required rational number is

15/20

Answer 2

Answer:

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

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

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

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Hence,

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Numerator, 3x = 3(5) = 15

Denominator, 4x = 4(5) = 20

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