Question

Two numbers are in ratio P:Q. when 1 is added to both the numerator and the denominator, the ratio gets changed to R/S. again, when 1 is added to both the numerator and denominator, it becomes 1/2. Find the sum of P and Q.
A.3
B.4
C.5
D.6

Answer 1

Given :

The two numbers are in ratio P : Q

when 1 is added to both the numerator and the denominator, the ratio gets changed to $\dfrac{R}{S}$

And

when 1 is added to both the numerator and denominator, it becomes $\dfrac{1}{2}$

To Find :

The sum of P and Q

Solution :

Statement I

when 1 is added to both the numerator and the denominator, the ratio gets changed to $\dfrac{R}{S}$

i.e   $\dfrac{P+1}{Q+1}$ = $\dfrac{R}{S}$               ..............1

Statement II

when 1 is added to both the numerator and denominator, it becomes $\dfrac{1}{2}$

i.e   $\dfrac{P+1 + 1}{Q+1 + 1}$  = $\dfrac{1}{2}$      

or, $\dfrac{P+2}{Q+2}$  = $\dfrac{1}{2}$      

Or,  2 P  + 4 = Q + 2

Or,  Q - 2 P = 4 - 2

Or,  Q - 2 P = 2

Or,  Q = 2 + 2 P

Now, Applying hit and trail method

for P  = 1  ,    Q = 2 + 2 × 1 = 4

So, P + Q = 1 + 4 = 5

 for P  = 2  ,    Q = 2 + 2 × 2 = 6

So, P + Q = 2 + 6 = 8

Thus, Condition which satisfy =  for P  = 1  , Q = 4  And, P + Q = 1 + 4 = 5

Hence, The sum of P and Q is 5   Answer