Pooja, Shipra and Monika are three sisters. Pooja and Shipra are twins. The ratio of sum of the ages of Pooja and Shipra is same as that of Monika alone. Three years earlier the ratio of age of Pooja and Monika was 2:7. What will be the age of Shipra 3 years hence?

Options

A. 21 years
B. 16 years
C. 8 years
D. 12 years

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define Variables
Let the present age of Pooja be \( P \) and since Pooja and Shipra are twins, the present age of Shipra will also be \( P \). Let the present age of Monika be \( M \).

### Step 2: Set Up the Ratio from the Past
According to the problem, three years ago, the ratio of the ages of Pooja and Monika was 2:7. Therefore, we can express their ages three years ago as:
- Pooja's age three years ago: \( P - 3 \)
- Monika's age three years ago: \( M - 3 \)

From the given ratio, we can write:
\[ \frac{P - 3}{M - 3} = \frac{2}{7} \]

### Step 3: Cross Multiply to Eliminate the Fraction
Cross multiplying gives us:
\[ 7(P - 3) = 2(M - 3) \]
Expanding both sides:
\[ 7P - 21 = 2M - 6 \]
Rearranging gives:
\[ 7P - 2M = 15 \quad \text{(Equation 1)} \]

### Step 4: Set Up the Current Age Ratio
The problem states that the ratio of the sum of the ages of Pooja and Shipra to Monika's age is 1:1. Therefore:
\[ \frac{P + P}{M} = 1 \]
This simplifies to:
\[ \frac{2P}{M} = 1 \]
Cross multiplying gives:
\[ 2P = M \quad \text{(Equation 2)} \]

### Step 5: Substitute Equation 2 into Equation 1
Now we can substitute \( M \) from Equation 2 into Equation 1:
\[ 7P - 2(2P) = 15 \]
This simplifies to:
\[ 7P - 4P = 15 \]
\[ 3P = 15 \]
\[ P = 5 \]

### Step 6: Find Monika's Age
Using \( P = 5 \) in Equation 2:
\[ M = 2P = 2(5) = 10 \]

### Step 7: Find Shipra's Present Age
Since Shipra is the same age as Pooja, Shipra's present age is:
\[ \text{Shipra's age} = P = 5 \]

### Step 8: Calculate Shipra's Age 3 Years Hence
To find Shipra's age three years hence:
\[ \text{Shipra's age in 3 years} = 5 + 3 = 8 \]

### Final Answer
The age of Shipra three years hence will be **8 years**.

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