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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

This Question Belongs to Arithmetic Ability >> Ratio

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Comments ( 4 )

  1. Vanlal Sanga
    Vanlal Sanga :
    2 years ago

    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

  2. Rakesh Chodapaneedi
    Rakesh Chodapaneedi :
    3 years ago

    >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.....

  3. Onno Jogot
    Onno Jogot :
    6 years ago

    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

  4. Shakur Fakir
    Shakur Fakir :
    6 years ago

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

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