5 yr ago, the average age of Rashmi and Surbhi was 20 yr. Now, the average age of Rashmi, Surbhi and Meeta is 30 yr. What will be the age of Meeta after 15 yr?

Options

A. 35yr
B. 55yr
C. 59yr
D. 67yr

Answer

To solve the problem step by step, we will break down the information given and calculate the ages accordingly.

### Step 1: Determine the total age of Rashmi and Surbhi 5 years ago.
The average age of Rashmi and Surbhi 5 years ago was 20 years. Since the average age is calculated as the total age divided by the number of individuals, we can find the total age of Rashmi and Surbhi at that time.

\[ \text{Average age} = \frac{\text{Total age}}{\text{Number of individuals}} \]

Let the total age of Rashmi and Surbhi 5 years ago be \( T \).

\[ 20 = \frac{T}{2} \]

Multiplying both sides by 2 gives:

\[ T = 40 \text{ years} \]

### Step 2: Calculate their current total age.
Since this was 5 years ago, we need to add 5 years for each of them to find their current total age.

\[ \text{Current total age of Rashmi and Surbhi} = 40 + 5 + 5 = 50 \text{ years} \]

### Step 3: Determine the total age of Rashmi, Surbhi, and Meeta now.
We know that the average age of Rashmi, Surbhi, and Meeta now is 30 years. Let’s denote the total age of Rashmi, Surbhi, and Meeta as \( T_m \).

\[ 30 = \frac{T_m}{3} \]

Multiplying both sides by 3 gives:

\[ T_m = 90 \text{ years} \]

### Step 4: Calculate Meeta's current age.
We already calculated the current total age of Rashmi and Surbhi as 50 years. Now we can find Meeta's current age by subtracting the total age of Rashmi and Surbhi from the total age of all three.

\[ \text{Current age of Meeta} = T_m - \text{Current total age of Rashmi and Surbhi} \]

\[ \text{Current age of Meeta} = 90 - 50 = 40 \text{ years} \]

### Step 5: Calculate Meeta's age after 15 years.
To find out how old Meeta will be in 15 years, we simply add 15 to her current age.

\[ \text{Age of Meeta after 15 years} = \text{Current age of Meeta} + 15 \]

\[ \text{Age of Meeta after 15 years} = 40 + 15 = 55 \text{ years} \]

### Final Answer:
Meeta will be 55 years old after 15 years.

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