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

To Find:-

• Find the rational number.

Given:-

• 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.

Solution:-

Let the numerator be " 3x "

Then denominator be " 4x "

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

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

$\tt\implies \: 5( 3x - 3 ) = 3( 4x )$

$\tt\implies \: 15x - 15 = 12x$

$\tt\implies \: 15x - 12x = 15$

$\tt\implies \: 3x = 15$

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

$\tt\implies \: x = 5$

Hence,

• $\tt \: Numerator \: \: is \: \: 3x - 3 = 12$

• $\tt \: Denominator \: \: is \: \: 4x = 20$