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 What is definitely the difference between R and Q's age ?

Options

A. 1 year
B. 2 years
C. 25 years
D. Data inadeuate

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the relationships between the ages
We know that:
- Q is as much younger than R as he is older than T.
- This means that the difference in age between R and Q is the same as the difference in age between Q and T.

### Step 2: Set up the equations
Let:
- Age of R = R
- Age of Q = Q
- Age of T = T

From the problem, we can express the relationships as:
1. R - Q = Q - T (This shows that the difference between R and Q is equal to the difference between Q and T)

### Step 3: Use the given information about the sum of ages
We are given that the sum of the ages of R and T is 50:
- R + T = 50

### Step 4: Substitute T in terms of R and Q
From the equation R - Q = Q - T, we can rearrange it to find T:
- T = 2Q - R

Now, substitute T in the sum equation:
- R + (2Q - R) = 50
- This simplifies to 2Q = 50
- Therefore, Q = 25

### Step 5: Find R and T using Q
Now that we have Q, we can find R and T:
- Substitute Q back into the equation for T:
- T = 2(25) - R
- T = 50 - R

Using the sum equation R + T = 50:
- R + (50 - R) = 50
- This is always true, indicating that R can be any value as long as T complements it to 50.

### Step 6: Find the difference between R and Q
Since we know Q = 25, we can express the difference:
- The difference between R and Q is |R - Q| = |R - 25|

### Step 7: Determine the definite difference
From the earlier relationship, we know that:
- R - Q = Q - T
- Therefore, the difference between R and Q is always 25 years.

Thus, the definite difference between R and Q's age is **25 years**.

### Final Answer
The difference between R and Q's age is **25 years**.