The denominator of a fraction exceeds the numerator by 2. If 5 be added to the numerator, the fraction increases by unity. The fraction is:
(a) 3/5
(b) 1/3
(c) 7/9
(d) None of these

To solve the problem, let's define the variables and equations based on the information given:

Let the numerator of the fraction be x .
Since the denominator exceeds the numerator by 2, the denominator is x + 2 .

So, the fraction is initially x + 2 x ​ .
According to the problem, if 5 is added to the numerator, the fraction increases by unity (which means by 1). Therefore, the new fraction is:
x + 2 x + 5 ​ = x + 2 x ​ + 1
We can now express this situation with an equation to find x :
x + 2 x + 5 ​ = x + 2 x ​ + 1
Subtract x + 2 x ​ from both sides:
x + 2 x + 5 ​ − x + 2 x ​ = 1
This simplifies to:
x + 2 ( x + 5 ) − x ​ = 1
x + 2 5 ​ = 1
Cross-multiply to remove the fraction:
5 = x + 2
Solve for x :
x = 5 − 2
x = 3
Now that we have x = 3 , substitute it back to find the denominator:
x + 2 = 3 + 2 = 5
The fraction is 5 3 ​ .
Therefore, the correct answer is option (a) 5 3 ​ .

Answered by OliviaMariThompson | 2025-07-21