Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is the difference between R and Q's age?

Explanation

Given:

- Q is as much younger than R as he is older than T  

  ⇒ R - Q = Q - T  

  ⇒ Rearranged: R + T = 2Q ...(1)

Also given:

- R + T = 50 ...(2)

From (1) and (2):  

2Q = 50 ⇒ Q = 25

Now put Q = 25 into equation:  

R + T = 50  

So, we still don’t know individual values of R or T, but we can find difference between R and Q:

From earlier:  

R - Q = Q - T  

⇒ R - 25 = 25 - T  

⇒ R + T = 50 (same again)

Now solve:  

R - 25 = 25 - T  

Add both sides:  

R - 25 + T = 25  

⇒ R + T = 50 

So we get consistent results.

Now, what is R - Q?  

Let’s find R:  

From earlier:

R - 25 = 25 - T ⇒ R = 50 - T

Now R - Q = R - 25 = (50 - T) - 25 = 25 - T

So unless T is given, we can’t determine exact value of R - Q

Correct Answer: D) Data inadequate 

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