Question

A fraction is such that numerator is 2 less than denominator.if u add 3 to numerator and 5 to denominator resulting fraction is equivalent to original fraction. find fraction

Answer 1

Let the denominator of the fraction be x
Now, According to question
Numerator is 2 times less than denominator. Therefore The fraction we get is -
x-2/x
After adding 3 to numerator and 5 to the denominator resulting fraction is equals to the original fraction -
therefore -
x-2+3/x+5 = x-2/x
x+1/x+5 = x-2/x
Now by cross multiplication
(x+1)(x) = (x-2)(x+5)
x^2 + x = x^2 + 5x - 2x - 10
x = 5x - 2x - 10
x = 3x - 10
x - 3x = -10
-2x = -10
x = -10/-2
x = 5
Verification -
By putting the value of x we get -
5-2+3/5+5 = 5-2/5
3+3/10 = 3/5
6/10 = 3/5
3/5 = 3/5

Therefore the fraction is 3/5

Hope this will help you dear

Answer 2

Solution -  

Let the dinominator be x  

So, the numerator be x - 2

 According to Question,  

x - 2 + 3/x + 5 = 3/5  

⇒ x + 1/x + 5 = 3/5  

⇒ 5(x + 1) = 3(x + 5)  

⇒ 5x + 5 = 3x + 15  

⇒ 5x - 3x = 15 - 5  

⇒ 2x = 10  

⇒ x = 10/2 = 5  

∵ Numerator = x - 2  = 5 - 2 = 3  

∵ Dinominator = x = 5  

∴ The fraction is 3/5.