5 years ago, the average age of P and Q was 15 years. Average age of P, Q and R today Is 20 years. How old will R be after 10 years?

Options

A. 35 years
B. 40 years
C. 30 years
D. 50 years

Answer

To solve the problem step by step, we will use the information given in the question about the average ages of P, Q, and R.

### Step 1: Determine the total age of P and Q 5 years ago.
Given that the average age of P and Q 5 years ago was 15 years, we can use the average formula:

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

Let the sum of the ages of P and Q 5 years ago be \( S \). Since there are 2 people (P and Q), we can set up the equation:

\[ 15 = \frac{S}{2} \]

Multiplying both sides by 2 gives:

\[ S = 30 \text{ years} \]

### Step 2: Determine the current total age of P and Q.
Since this information is from 5 years ago, we need to add 5 years to each of their ages to find their current total age:

\[ \text{Current total age of P and Q} = S + 5 + 5 = 30 + 10 = 40 \text{ years} \]

### Step 3: Determine the total age of P, Q, and R today.
We know that the average age of P, Q, and R today is 20 years. Using the average formula again, we can express the total age of P, Q, and R as follows:

Let \( T \) be the total age of P, Q, and R today. Since there are 3 people, we have:

\[ 20 = \frac{T}{3} \]

Multiplying both sides by 3 gives:

\[ T = 60 \text{ years} \]

### Step 4: Determine the current age of R.
We already calculated the current total age of P and Q to be 40 years. Therefore, we can find R's current age by subtracting the total age of P and Q from the total age of P, Q, and R:

\[ \text{Current age of R} = T - \text{Current total age of P and Q} = 60 - 40 = 20 \text{ years} \]

### Step 5: Determine R's age after 10 years.
To find R's age after 10 years, we simply add 10 years to R's current age:

\[ \text{Age of R after 10 years} = \text{Current age of R} + 10 = 20 + 10 = 30 \text{ years} \]

### Final Answer:
R will be 30 years old after 10 years.

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