The ages of Mira, Tina and Sania are in the ratio of 6 : 4 : 7, respectively. If the sum of their ages is 34 years. what is sania's age ?

Options

A. 12
B. 20
C. 14
D. can't be determined

Answer

To solve the problem of finding Sania's age given the ages of Mira, Tina, and Sania are in the ratio of 6:4:7 and their total age sums to 34 years, we can follow these steps:

### Step 1: Understand the Ratio
The ages of Mira, Tina, and Sania are given in the ratio of 6:4:7. This means:
- Mira's age = 6 parts
- Tina's age = 4 parts
- Sania's age = 7 parts

### Step 2: Assign Variables
To make calculations easier, we can assign a variable \( x \) to represent the common multiple of their ages. Thus, we can express their ages as:
- Mira's age = \( 6x \)
- Tina's age = \( 4x \)
- Sania's age = \( 7x \)

### Step 3: Set Up the Equation
According to the problem, the sum of their ages is 34 years. Therefore, we can set up the following equation:
\[ 6x + 4x + 7x = 34 \]

### Step 4: Combine Like Terms
Now, combine the terms on the left side:
\[ (6x + 4x + 7x) = 17x \]
So, we have:
\[ 17x = 34 \]

### Step 5: Solve for \( x \)
To find the value of \( x \), divide both sides of the equation by 17:
\[ x = \frac{34}{17} = 2 \]

### Step 6: Calculate Sania's Age
Now that we have the value of \( x \), we can find Sania's age:
\[ \text{Sania's age} = 7x = 7 \times 2 = 14 \]

### Final Answer
Sania's age is **14 years**.

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