The average of the ages of Sumit, Krishna and Rishabh is 43 years and the average of the ages of Sumit, Rishabh and Rohit is 49 years. If Rohit is 54 years old, what is Krishna'a age ?

Options

A. A. 48 yrs
B. B. 42 yrs
C. C. 40 yrs
D. D. 36 yrs

Answer

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

**Step 1: Understand the given information.**
- The average age of Sumit, Krishna, and Rishabh is 43 years.
- The average age of Sumit, Rishabh, and Rohit is 49 years.
- Rohit is 54 years old.

**Step 2: Set up equations based on the averages.**
Let the ages of Sumit, Krishna, and Rishabh be represented as S, K, and R respectively.

From the first average:
\[ \frac{S + K + R}{3} = 43 \]
Multiplying both sides by 3 gives:
\[ S + K + R = 129 \quad \text{(Equation 1)} \]

From the second average:
\[ \frac{S + R + 54}{3} = 49 \]
Multiplying both sides by 3 gives:
\[ S + R + 54 = 147 \]
Subtracting 54 from both sides gives:
\[ S + R = 93 \quad \text{(Equation 2)} \]

**Step 3: Substitute Equation 2 into Equation 1.**
We can substitute \(S + R\) from Equation 2 into Equation 1:
\[ 93 + K = 129 \]
Now, solve for K:
\[ K = 129 - 93 \]
\[ K = 36 \]

**Step 4: Conclusion.**
Krishna's age is 36 years.

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