There are four people P, Q, R and S. R and P are the oldest and youngest among them. Q is older than S. The present age of R is double the present age of P. Which of the following statements is/are sufficient to obtain the age of Q, ‘y’ years ago?

(i) The ratio between the present ages of R and S is 4:3 respectively.

(ii) Four years hence, the average of the present ages of P and Q is 18 years.

(iii) ‘y’ years hence, the age of Q is equal to the present age of R.

Solution

There are four people P, Q, R and S. R and P are the oldest and youngest among them. Q is older than S. Let’s assume the present ages of P, Q, R and S are ‘p’, ‘q’, ‘r’ and ‘s’ respectively. So r>q>s>p    Eq.(i) The present age of R is double the present age of P. r = 2p    Eq.(ii) (i) The ratio between the present ages of R and S is 4:3 respectively. Let’s assume r = 4a and s = 3a. From Eq.(ii), 2p = r, then 2p = 4a So p = 2a Here no information about the age of Q and the variable ‘y’ is available. So this statement is not sufficient to answer the question. (ii) Four years hence, the average of the present ages of P and Q is 18 years. (p+q+4+4)/2 = 18 (p+q+4+4) = 36 (p+q+8) = 36 p+q = 36-8 (p+q) = 28 Here no information about the variable ‘y’ is available. So this statement is not sufficient to answer the question. (iii) ‘y’ years hence, the age of Q is equal to the present age of R. q+y = r From the given information, the required answer cannot be obtained. So this statement is not sufficient to answer the question. Only (i) & (ii) (p+q) = 28 (2a+q) = 28 q = (28-2a) From the given information, the required answer cannot be obtained. So these statements are not sufficient to answer the question. Only (ii) & (iii) Here three variables are available with the least information. So from the given information, the required answer cannot be obtained. Hence these statements are not sufficient to answer the question. Only (i) & (iii) Here four variables are available with the least information. From the given information, the required answer cannot be obtained. So these statements are not sufficient to answer the question. All (i), (ii) & (iii) From the given information, the required answer cannot be obtained. So these statements are not sufficient to answer the question. (28-2a) + y = 4a