Question

The denominator of a rational number is 4 less than twice the numerator. If the numerator is increased by 5 and the denominator is decreased by 6, the number obtained is . Find the rational number .

Answer 1

Correct Question:

• The denominator of a rational number is 4 less than twice the numerator. If the numerator is increased by 5 and the denominator is decreased by 6, the number obtained is ⅗. Find the rational number.

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AnswEr :

☯ Let's say, that the numerator be x and then denominator be (2x – 4).

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$\underline{\bigstar\:{\textsf{According to the given Question :}}}$⠀⠀

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$:\implies\tiny\tt\dfrac{Numerator + 5}{Denominator - 6} = New \; number \: \dfrac{3}{5} \\\\\\:\implies\tt\dfrac{x + 5}{(2x - 4) - 6} = \dfrac{3}{5} \\\\\\:\implies\tt 5\Big(x + 5\Big) = 3\Big(2x - 4 - 6\Big) \\\\\\:\implies\tt 5x + 25 = 3\Big(2x - 10\Big) \\\\\\:\implies\tt 5x + 25 = 6x - 30\\\\\\:\implies\tt 5x - 6x = -30 - 25\\\\\\:\implies\tt -x = -55\\\\\\:\implies\underline{\boxed{\pmb{\frak{\red{x = 55}}}}}\;\bigstar$

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Therefore,

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• Numerator of the fraction, x = 55.
• Denominator of the fraction, (2x – 4) = (2 [55] – 4) = 106.

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$\therefore{\underline{\sf{Hence,\; the\; required\; rational \:number \;is\; {\pmb{\sf{\dfrac{55}{106}}}}.}}}$

Answer 2

Given :-

The denominator of a rational number is 4 less than twice the numerator. If the numerator is increased by 5 and the denominator is decreased by 6, the number obtained is 3/5

To Find :-

Rational number

Solution :-

Let the numerator be y = y/2y - 4

Now

When 5 added to numerator and denominator decreased by 6

According to the question

y + 5/2y - 4 - 6 = 3/5

y + 5/2y - 10 = 3/5

5(y + 5) = 3(2y - 10)

5y + 25 = 6y - 30

5y - 6y = -30 - 25

-y = -55

y = 55

And

Denominator = 2y - 4 = 2(55) - 4 = 106

Fraction = 55/106

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