Two numbers are in ratio P : Q. when 1 is added to both the numerator and the denominator, the ratio gets changed to $$\frac{{\text{R}}}{{\text{S}}}$$. again, when 1 is added to both the numerator and denominator, it becomes $$\frac{1}{2}$$. Find the sum of P and Q.
a) 3
b) 4
c) 5
d) 6

Answer: c
Explanation: We will solve this question through options
Taking Option A:
It has P + Q = 3.
The possible value of $$\frac{{\text{P}}}{{\text{Q}}}$$ is $$\frac{1}{2}$$ or $$\frac{2}{1}$$
Using $$\frac{1}{2}$$, we see that on adding 2 in both the numerator and denominator we get $$\frac{3}{4}$$ (not required value)
Similarly we check for $$\frac{2}{1}$$, this will also not give the required value
Option B:
We have $$\frac{1}{3}$$ possible ratio
Then, we get the final value as $$\frac{3}{5}$$ (not = to $$\frac{1}{2}$$)
Hence, rejected
Option C:
Here we have $$\frac{1}{4}$$ or $$\frac{2}{3}$$
Checking for $$\frac{1}{4}$$ we get $$\frac{3}{6}$$ = $$\frac{1}{2}$$
Hence, the option c is correct