The ratio of runs scored by Dhawan and Virat in a one-day cricket match is `5:7.` If Virat sscored 77 runs find the sum of runs scored by both.

Options

A. `189`
B. `156`
C. `135`
D. `132`

Answer

To solve the problem, we need to find the runs scored by Dhawan and then calculate the total runs scored by both Dhawan and Virat.

### Step-by-Step Solution:

1. **Understand the Ratio**: The ratio of runs scored by Dhawan to Virat is given as \(5:7\). This means for every 5 runs Dhawan scores, Virat scores 7 runs.

2. **Identify the Runs Scored by Virat**: We know that Virat scored 77 runs.

3. **Set Up the Equation**: Since the ratio of Dhawan's runs to Virat's runs is \(5:7\), we can express Dhawan's runs (D) in terms of Virat's runs (V):
\[ \frac{D}{V} = \frac{5}{7} \]
Substituting the value of V (Virat's runs):
\[ \frac{D}{77} = \frac{5}{7} \]

4. **Cross-Multiply to Find Dhawan's Runs**:
\[ D \cdot 7 = 5 \cdot 77 \]
\[ 7D = 385 \]

5. **Solve for D**:
\[ D = \frac{385}{7} \]
\[ D = 55 \]
So, Dhawan scored 55 runs.

6. **Calculate the Total Runs Scored by Both**:
\[ \text{Total Runs} = D + V = 55 + 77 \]
\[ \text{Total Runs} = 132 \]

### Final Answer:
The sum of runs scored by both Dhawan and Virat is **132**.

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