Ratio between age of priya and Swati is 3:4. If shikha is 6 year younger than swati and average age of all three is 31 years, then find Shikha's age?

Options

A. 36 yrs
B. 32 yrs
C. 20 yrs
D. 30 yrs

Answer

To find Shikha's age, we can follow these steps:

### Step 1: Define the Variables
Let the age of Priya be \(3x\) and the age of Swati be \(4x\), based on the ratio given (3:4).

### Step 2: Express Shikha's Age
Since Shikha is 6 years younger than Swati, we can express Shikha's age as:
\[ \text{Shikha's age} = 4x - 6 \]

### Step 3: Calculate the Average Age
The average age of Priya, Swati, and Shikha is given as 31 years. Therefore, we can set up the equation:
\[ \frac{3x + 4x + (4x - 6)}{3} = 31 \]

### Step 4: Simplify the Equation
Combine the ages in the numerator:
\[ \frac{3x + 4x + 4x - 6}{3} = 31 \]
This simplifies to:
\[ \frac{11x - 6}{3} = 31 \]

### Step 5: Eliminate the Denominator
Multiply both sides by 3 to eliminate the fraction:
\[ 11x - 6 = 93 \]

### Step 6: Solve for \(x\)
Add 6 to both sides:
\[ 11x = 99 \]
Now, divide by 11:
\[ x = 9 \]

### Step 7: Find the Ages
Now that we have \(x\), we can find the ages:
- Priya's age: \(3x = 3 \times 9 = 27\)
- Swati's age: \(4x = 4 \times 9 = 36\)
- Shikha's age: \(4x - 6 = 36 - 6 = 30\)

### Conclusion
Shikha's age is:
\[ \text{Shikha's age} = 30 \text{ years} \]

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