Question

the original
2
In a fraction, twice the numerator is 2 more than the denominator. If 3 is adde
numerator and to the denominator, the new fraction is2/3
Find the original fraction ​

Answer 1

Given:

• In a fraction, twice the numerator is 2 more than the denominator. If 3 is added numerator and to the denominator, the new fraction is 2/3.

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To find:

• Original Fraction?

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Solution:

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☯ Let Numerator of a fraction be x.

Then, The Denominator will be (2x - 2).

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

• If 3 is added numerator and to the denominator, the new fraction is 2/3.

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$:\implies\sf \dfrac{x + 3}{(2x - 2) + 3} = \dfrac{2}{3}$

$:\implies\sf \dfrac{x + 3}{2x + 1} = \dfrac{2}{3}$

$:\implies\sf 3(x + 3) = 2(2x + 1)$

$:\implies\sf 3x + 9 = 4x + 2$

$:\implies\sf 4x - 3x = 9 - 2$

$:\implies{\underline{\boxed{\sf{\purple{x = 7}}}}}\;\bigstar$

Therefore,

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• $\sf Numerator,\:x = \bf{7}$
• $\sf Denominator,\:(2x - 2) = 2 \times 7 - 2 = 14 - 2 = \bf{12}$

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$\therefore\:{\underline{\sf{Hence,\;the\;original\;fraction\:is\; \bf{ \dfrac{7}{12}}.}}}$

Answer 2

Answer:

Given :-

In a fraction, twice the numerator is 2 more than the denominator. If 3 is added numerator and to the denominator, the new fraction is 2/3.

To Find :-

Original fraction

Solution :-

Let the numerator be x

$\sf \: original \: fraction = \dfrac{x}{2x - 2}$

$\sf \: new \: fraction = \dfrac{x + 3}{2x - 2 + 3} = \dfrac{2}{3}$

$\sf \: By \: cross \: multiplication \:$

$\sf \: 3(x + 3) = 2(2x + 1)$

$\sf \: 3 \times x + 3 \times 3 = 2 \times x + 2 \times 1$

$\sf \: 3x + 9 = 4x + 2$

$\sf \: 4x - 3x = 9 - 2$

$\sf \: x = 9 - 2$

$\sf \: x = 7$

Now,

Let's find denominator

$\dfrac{ \sf \: 7}{ \sf \: 2(7) - 2} = \dfrac{7}{14 - 2} = \dfrac{7}{12}$

Hence,

Original fraction is

$\huge \bf \: = \frac{7}{12}$