The sum of the numerator and denominator of a fraction is 4 more than

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

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

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 .