Question

Q. In a fraction, twice the numerator is 2 more than the dinominator. If 3 is added to the numerator and to the dinominator, the new fraction is 2/3. Find the original fraction.

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Answer 1

Hello!

Here is your answer!
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▶️ Let the numerator be x and denominator be y

Twice the numerator = 2x 

Given 2x = y + 2

That is 2x – 2 = y ... (1)

Original fraction = x/y

Given (x + 3)/(y + 3) = 2/3

▶️ 3x + 9 = 2y + 6

▶️ 3x + 9 = 2 ( 2x - 2 ) + 6 [ From (1) ]

▶️ 3x + 9 = 4x – 4 + 6

▶️ x = 7

Therefore, y = 12 [ 2 × 7 - 2 [ From ( 1 ) ]

Original fraction = 7/12√√

Hope it helps you!☺

Answer 2

Let the numerator be x denominator be y

then according to the question,

2x = y + 2
y = 2x - 2

also given,
$\frac{x + 3}{y + 3} = \frac{2}{3}$
or we can write y as 2x - 2

=>
$\frac{x + 3}{2x - 2 + 3} = \frac{2}{3} \\ \\ = > \frac{x + 3}{2x + 1} = \frac{2}{3}$


By cross multiplication we get


3(x + 3) = 2(2x + 1)

=> 3x + 9 = 4x + 2

=> 3x - 4x = 2 - 9

=> -(x) = -(7)

=> x = 7


so denominator y = 2x - 2


=> 2(7) - 2

=> 14 - 2
=> 12

Hence, the required fraction is 7/12
$\frac{7}{12}$
Hope it helps dear friend ☺️✌️