Question

solve the above question that carries 4 marks​

Answer 1

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

Answer:

5/9

Step-by-step explanation:

Let the denominator be 'x' and numerator be 'y'.  Hence, the fraction is y/x

According to the question:

Case 1:         ⇒ x + y = 4 + 2y

⇒ x = 4 + y         ...(1)

Case 2: If both are increased by 3,

denominator = x + 3 and numerator = y + 3

Ratio is 2 : 3.

⇒ (y + 3)/(x + 3) = 2/3

⇒ 3(y + 3) = 2(x + 3)

⇒ 3y + 9 = 2x + 6  

         from (1)

⇒ 3y + 9 - 6 = 2(4 + y)

⇒ 3y + 3 = 8 + 2y

⇒ 3y - 2y = 8 - 3 = 5

⇒ y = 5

  hence,

x = 4 + y = 4 + 5 = 9

 Therefore, the fraction is:

fraction = y/x  = 5/9

Fraction is 5/9