Math, asked by sejalkumari9a, 3 months ago

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.​

Answers

Answered by Anonymous
44

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...

Answered by ShírIey
102

☯ 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}}.}}}

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