The average age of P,Q, R and S is 30 years. How old is R ?
(i) The sum of ages of P and R is 60 years
(ii) S is 10 years younger than R.

Answer

To solve the problem step by step, we will analyze the information provided and derive the age of R.

### Step 1: Calculate the total sum of ages of P, Q, R, and S.
Given that the average age of P, Q, R, and S is 30 years, we can calculate the total sum of their ages.

\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of individuals}} \]

Let the sum of ages of P, Q, R, and S be \( S \).

\[ 30 = \frac{S}{4} \]

Multiplying both sides by 4 gives:

\[ S = 30 \times 4 = 120 \]

So, the total sum of ages of P, Q, R, and S is 120 years.

### Step 2: Analyze the first piece of information.
The first piece of information states that the sum of the ages of P and R is 60 years.

Let’s denote:
- Age of P = \( P \)
- Age of R = \( R \)

From the information given:

\[ P + R = 60 \]

### Step 3: Analyze the second piece of information.
The second piece of information states that S is 10 years younger than R.

Let’s denote:
- Age of S = \( S \)

From this information, we can express S in terms of R:

\[ S = R - 10 \]

### Step 4: Substitute the values into the total sum equation.
Now we know:
- Total sum of ages \( P + Q + R + S = 120 \)
- From Step 2, \( P + R = 60 \)
- From Step 3, \( S = R - 10 \)

Now, substituting \( S \) into the total sum equation:

\[ P + Q + R + (R - 10) = 120 \]

This simplifies to:

\[ P + Q + 2R - 10 = 120 \]

### Step 5: Substitute \( P + R \) into the equation.
We know \( P + R = 60 \), so we can express \( P \) as \( P = 60 - R \).

Substituting this into the equation gives:

\[ (60 - R) + Q + 2R - 10 = 120 \]

This simplifies to:

\[ 60 - R + Q + 2R - 10 = 120 \]

Combining like terms:

\[ Q + R + 50 = 120 \]

### Step 6: Solve for Q.
Now we can isolate Q:

\[ Q + R = 120 - 50 \]
\[ Q + R = 70 \]

### Step 7: Analyze the equations.
Now we have two equations:
1. \( P + R = 60 \)
2. \( Q + R = 70 \)

From these equations, we can see that we have two variables (P and Q) and two equations, but we do not have enough information to find the exact value of R.

### Conclusion:
Since we cannot determine the exact age of R from the given information, the answer is that it is not possible to find the age of R.

---