The average of the runs made by Raju, Shyam and Hari is 7 less than that made by Shyam, Hari and Kishore. If the number of Kishore's run is 35, what is Raju's run ?

Options

A. 14
B. 21
C. 35
D. 7

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information given.

### Step 1: Define the variables
Let:
- R = Raju's runs
- S = Shyam's runs
- H = Hari's runs
- K = Kishore's runs = 35 (given)

### Step 2: Set up the equations for averages
According to the problem, the average of the runs made by Raju, Shyam, and Hari is 7 less than the average of the runs made by Shyam, Hari, and Kishore.

The average of Raju, Shyam, and Hari can be expressed as:
\[ \text{Average}_{R, S, H} = \frac{R + S + H}{3} \]

The average of Shyam, Hari, and Kishore can be expressed as:
\[ \text{Average}_{S, H, K} = \frac{S + H + K}{3} \]

### Step 3: Write the equation based on the problem statement
From the problem statement, we have:
\[ \frac{R + S + H}{3} = \frac{S + H + K}{3} - 7 \]

### Step 4: Eliminate the denominators
To eliminate the denominators, we can multiply both sides of the equation by 3:
\[ R + S + H = S + H + K - 21 \]

### Step 5: Substitute the value of K
Since K = 35, we substitute this value into the equation:
\[ R + S + H = S + H + 35 - 21 \]
\[ R + S + H = S + H + 14 \]

### Step 6: Simplify the equation
Now, we can simplify the equation by subtracting S and H from both sides:
\[ R = 14 \]

### Conclusion
Thus, Raju's runs are:
\[ \text{Raju's runs} = 14 \]