Question

A fraction is such that if the numerator is multiplied by 3 and the denominator is
reduced by 3, we get 3/2, but if the numerator is increased by 8 and denominator is
doubled, we get 5/7. Find the fraction​

Answer 1

Answer:

Step-by-step explanation:

Solution :-

Let the fraction be x/y.

Then,

According to the question

3x/y - 3 = 18/11

and x + 8/2y = 2/5

⇒ 11x = 6y - 18 and 5x + 40 = 4y

⇒ 11x - 6y + 18 = 0 and 5x - 4y + 40 = 0

By cross-multiplication. we get

⇒ x/(- 6) × 40 - (- 4) × 18 = - y/11 × 40 - 5 × 18 = 1/11 × (- 4) - 5 × (- 6)

⇒ x/- 240 + 72 = - y/440 - 90 = 1/- 44 + 30

⇒ x/- 168 = y/- 350 = 1/- 14

⇒ x = - 168/- 14 and y = - 350/- 14

⇒ x = 12 and y = 25

Hence, the fraction is 12/25