Question

The sum of the numerator and denominator of a fraction is 4 more than twice the denominator. If the numerator and denominator are increased by 3, they are in the ratio 2:3. Determine the fraction.
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Answer 1

Answer:

Let the required fraction be x/y .

As per the question x + y = 4 + 2x

⇒ y – x = 4

(i) After changing the numerator and denominator

New numerator = x + 3

New denominator = y + 3

Therefore x+3/ y+3 = 2/3

⇒3(x + 3) = 2(y + 3)

⇒3x + 9 = 2y + 6

⇒ 2y – 3x = 3 ……

(ii) Multiplying

(i) by 3 and subtracting (ii),

we get: 3y – 2y = 12 – 3 ⇒y = 9

Now, putting y = 9 in (i),

we get: 9 – x = 4 ⇒ x = 9 – 4 = 5 Hence,

the required fraction is 5/9

Step-by-step explanation:

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