The average age of Rustam and Preetam is 39 years. The average age of Preetam and Geetam is 28 years. The average age of Rustam and Geetam is 34 years. What will be the age (in years) of the youngest of the three after 10 years?

Options

A. a) 13
B. b) 23
C. c) 33
D. d) 43

Answer

To solve the problem, we will set up equations based on the information given about the average ages of Rustam (R), Preetam (P), and Geetam (G).

### Step 1: Set up the equations based on the averages given.
1. The average age of Rustam and Preetam is 39 years:
\[ \frac{R + P}{2} = 39 \implies R + P = 78 \quad \text{(Equation 1)} \]

2. The average age of Preetam and Geetam is 28 years:
\[ \frac{P + G}{2} = 28 \implies P + G = 56 \quad \text{(Equation 2)} \]

3. The average age of Rustam and Geetam is 34 years:
\[ \frac{R + G}{2} = 34 \implies R + G = 68 \quad \text{(Equation 3)} \]

### Step 2: Solve the equations to find the ages.
We have the following equations:
- \( R + P = 78 \) (Equation 1)
- \( P + G = 56 \) (Equation 2)
- \( R + G = 68 \) (Equation 3)

#### Step 2.1: Find \( R - G \)
Subtract Equation 2 from Equation 1:
\[ (R + P) - (P + G) = 78 - 56 \]
This simplifies to:
\[ R - G = 22 \quad \text{(Equation 4)} \]

#### Step 2.2: Find \( R \)
Now, add Equation 3 and Equation 4:
\[ (R + G) + (R - G) = 68 + 22 \]
This simplifies to:
\[ 2R = 90 \implies R = 45 \]

#### Step 2.3: Find \( G \)
Substituting \( R = 45 \) into Equation 3:
\[ 45 + G = 68 \implies G = 68 - 45 = 23 \]

#### Step 2.4: Find \( P \)
Substituting \( G = 23 \) into Equation 2:
\[ P + 23 = 56 \implies P = 56 - 23 = 33 \]

### Summary of ages:
- Rustam (R) = 45 years
- Preetam (P) = 33 years
- Geetam (G) = 23 years

### Step 3: Determine the youngest age after 10 years.
The youngest among Rustam, Preetam, and Geetam is Geetam (G) who is currently 23 years old. After 10 years, Geetam's age will be:
\[ G + 10 = 23 + 10 = 33 \text{ years} \]

### Final Answer:
The age of the youngest of the three after 10 years will be **33 years**.

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