# 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: Option C **

__Solution(By Examveda Team)__

If we go through normal method, It will be quite cumbersome,so,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

Ater 1 is added 2 times to both numerator and denominator, we get the ratio as

(P+2)/(Q+2)= 1/2

=> 2P+4=Q+2

=> Q-2P=2

Possible values of Q and P are (4,1),(5,3),(6,4),......

here the only possible value from the given answers is (4,1) I.e. Q+P=5

>P+2/q+2=1/2

>2p+4=q+2q

>q-2p=2

>Let q=1

By changing p value from 1,2,3....we get -1,-3,-5 respectively we couldn't get 2.

>Let q=2

By changing p value from 1,2,3...we get 0,-2,-4... respectively we couldn't get 2.

Let q=3

By changing p value from 1,2,3....we get 1,-1,-3... respectively we couldn't get 2.

Let q=4

By changing p value from 1,2,3.....we get

at q=4&p=1

So sum=5.

Its very simple.....

We could approach backward.

Given final ratio 1/2 is found by adding 2 to both the numerator and denominator.

Hence, in this case, while going backward we will subtract 2 from denominator and numerator.

But, (1-2)/(2-2) = -1/0 ( we cannot do that.

So, we tried to modify the ratio by multiplying with same number.

1/2 = 2/4.

Now, let's try again,

(2-2)/(4-2)

but this time, numerator becomes zero.

So, we again modify the ratio 1/2 as 3/6 and then subtract 2 from each of the numbers.

(3-2)/(6-2) = 1/4

Therefore, P/Q = 1/4

(You can justify by adding 2 to both the numerator and the denominator, you will get 1/2.

Finally, the answer is 1+4 = 5

if this math come to written how can i solve this? pls give the solve of this problem.