Five years ago, the average age of P and Q was 15 yr. Now, average age of P, Q and R is 20 yr. What whould be the age of R after 10 yr?

Options

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

Answer

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

### Step 1: Determine the sum of ages of P and Q five years ago.
The average age of P and Q five years ago was 15 years. The formula for average is:

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

Let the sum of the ages of P and Q five years ago be \( S \). Since there are 2 people (P and Q):

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

Multiplying both sides by 2 gives:

\[ S = 30 \]

So, the sum of the ages of P and Q five years ago was 30 years.

### Step 2: Calculate the present ages of P and Q.
Since this sum was five years ago, we need to add 10 years to account for the passage of time (5 years for P and 5 years for Q):

\[ \text{Present age of P + Q} = 30 + 10 = 40 \]

### Step 3: Determine the sum of ages of P, Q, and R now.
Now, we know that the average age of P, Q, and R is 20 years. Let the sum of their ages be \( S' \):

\[ 20 = \frac{S'}{3} \]

Multiplying both sides by 3 gives:

\[ S' = 60 \]

So, the sum of the present ages of P, Q, and R is 60 years.

### Step 4: Find the present age of R.
We already calculated the present age of P and Q to be 40 years. Now we can find the age of R:

\[ \text{Present age of R} = S' - (\text{Present age of P + Q}) = 60 - 40 = 20 \]

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

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

### Final Answer:
The age of R after 10 years will be **30 years**.

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