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 optionsTaking 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
This Question Belongs to Arithmetic Ability >> Ratio
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.