Question

Q.12 The numerator of a rational number is 3 less than its denominator . If numerator is increased by 1 and denominator is increased by 3 then the number becomes 1 /2 Find the rational number.​

Answer 1

Step-by-step explanation:

n = d-3

{n+1}/d+3 = 1/2

2n+2 = d+3

2n-1 = n+3

n=4

d =7

4/7 answer...

Answer 2

☯ Let's consider that the Denominator be x.

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Given that,

• The numerator of a rational number is 3 less than its denominator.

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Therefore,

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$:\implies\sf Numerator = (x - 3)$

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

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• If numerator is increased by 1 and denominator is increased by 3 then the number becomes 1/2.

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$:\implies\sf \dfrac{(x - 3) + 1}{x + 3} = \dfrac{1}{2} \\\\\\:\implies\sf \dfrac{x - 2}{x + 3} = \dfrac{1}{2} \\\\\\:\implies\sf x + 3 = 2(x - 2)\\\\\\:\implies\sf x + 3 = 2x - 4\\\\\\:\implies\sf x - 2x = - 4 - 3\\\\\\:\implies\sf -x = -7\\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 7}}}}}$

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Hence,

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• Denominator, x = 7
• Numerator (x - 3), (7 - 3) = 4

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$\therefore\:{\underline{\sf{The\: required\:number\;is\: \bf{ \dfrac{4}{7}}.}}}$