Sum of numerator and denominator of a fraction is 13. Adding 3 and 9 to the numerator and denominator respectively, the fraction becomes 2/3. What is the product of the numerator and denominator of the original fraction?

Sum of numerator and denominator of a fraction is 13. Adding 3 and 9 to the numerator and denominator respectively, the fraction becomes 2/3. What is the product of the numerator and denominator of the original fraction? Correct Answer 42

Let the numerator and denominator by x and y respectively.

According to the question

x + y = 13        ---(1)

⇒ (x + 3)/(y + 9) = 2/3

⇒ 3 (x + 3) = 2 (y + 9)

⇒ 3x + 9 = 2y + 18

⇒ 3x - 2y = 18 - 9

3x - 2y = 9        ---(2)

Multiply by 2 in equation (1) and add in equation (2)

5x = 35

⇒ x = 35/5

⇒ x = 7

Put x = 7 in equation (1)

7 + y = 13

⇒ y = 13 - 7

⇒ y = 6

Product of numerator and denominator = 6 × 7 = 42

Short Trick:

Let the number be x and y respectively.

⇒ x + y = 13

Put x = 7 and y = 6 and satisfied the condition.