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1. Two numbers are in ratio P : Q. when 1 is added to both the numerator and the denominator, the ratio gets changed to $\frac{R}{S}$ . 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

Solution:

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{P}{Q}

\frac{1}{2}

\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}

\frac{2}{3}

Checking for

\frac{1}{4}

we get

\frac{3}{6}

\frac{1}{2}

Hence, the option c is correct

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