🤔 Age Difference Puzzle 🤓

Let’s break it down step by step:

Let Q’s age be x.

Since Q is as much younger than R as he is older than T, we can set up the following equation:

R – x = x – T

Simplifying the equation:

R + T = 2x

We know that the sum of R and T’s ages is 50:

R + T = 50

Substituting this into the previous equation:

50 = 2x

Dividing by 2:

x = 25

So Q’s age is 25.

Now, let’s find the difference between R and Q’s age:

R – Q = R – 25

We don’t know R’s exact age, but we can express it in terms of T:

R + T = 50

R = 50 – T

Substituting this into the previous equation:

(50 – T) – 25

Simplifying:

25 – T

Since T’s age is unknown, the difference between R and Q’s age can be any value.

However, we can determine the range of possible differences:

The maximum difference occurs when T is 0 (which is not possible in reality, but let’s consider it for the sake of calculation):

25 – 0 = 25

The minimum difference occurs when T is 25 (which would make Q and T the same age):

25 – 25 = 0

Since we’re looking for a definite difference, we can conclude that:

The difference between R and Q’s age is at least 5 years.

This is because the minimum possible age for T is 0 (which is not realistic), and the maximum possible age for T is 25. Any value of T between 0 and 25 would result in a difference of at least 5 years.

However, without knowing the exact ages of R and T, we cannot determine the exact difference.

But we can say that the difference between R and Q’s age is at least 5 years, and at most 25 years.