Question

By adding 3 and 5 in numerator and denominator of a fraction it becomes \(\frac{2}{3}\). If 1 and 3 are subtracted and added from numerator and denominator respectively it becomes \(\frac{2}{5}\) find the fraction.
1. \(\frac{6}{7}\)
2. \(\frac{7}{5}\)
3. \(\frac{5}{7}\)
4. \(\frac{7}{6}\)

Answer 1

Correct Answer - Option 3 : \(\frac{5}{7}\)

Given :

By adding 3 and 5 in the numerator and denominator a fraction becomes 2/3. 

By subtracting 1 from the numerator and adding 3 in the denominator fraction will become 2/5. 

Calculations :

Let the fraction be 'x/y'

According to the question 

(x + 3)/(y + 5) = 2/3 

⇒ 3x - 2y = 1      ....(1) 

Again 

(x - 1)/(y + 3) = 2/5 

⇒ 5x - 2y = 11      ....(2) 

Solving equation 1 and 2 

We get, x = 5 and y = 7 

Fraction = x/y 

⇒ 5/7 

∴ Option 3 will be the correct answer.