In a cricket match the total number of runs scored by Sachin, Vinod and Sourav is 285. The ratio of the number of runs scored by Sachin and Sourav is `3 :2` and that of the runs scored by Sourav and Vinod is also `3 : 2`. The number of runs scored by Sachin In that match Is

Options

A. 135
B. 90
C. 60
D. 140

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Variables
Let the number of runs scored by Sachin be \( S \), by Sourav be \( R \), and by Vinod be \( V \).

### Step 2: Set Up the Ratios
From the problem, we know:
- The ratio of runs scored by Sachin to Sourav is \( S : R = 3 : 2 \).
- The ratio of runs scored by Sourav to Vinod is \( R : V = 3 : 2 \).

### Step 3: Express Runs in Terms of a Common Variable
Using the ratios, we can express the runs in terms of a common variable:
- Let \( R = 2x \) (where \( x \) is a common multiplier).
- Then, from the first ratio \( S : R = 3 : 2 \), we have \( S = \frac{3}{2}R = \frac{3}{2}(2x) = 3x \).
- From the second ratio \( R : V = 3 : 2 \), we have \( V = \frac{2}{3}R = \frac{2}{3}(2x) = \frac{4}{3}x \).

### Step 4: Write the Total Runs Equation
According to the problem, the total runs scored by Sachin, Sourav, and Vinod is 285:
\[ S + R + V = 285 \]
Substituting the expressions we found:
\[ 3x + 2x + \frac{4}{3}x = 285 \]

### Step 5: Combine the Terms
To combine the terms, we need a common denominator. The common denominator for the terms is 3:
\[ \frac{9x}{3} + \frac{6x}{3} + \frac{4x}{3} = 285 \]
Combining the fractions:
\[ \frac{19x}{3} = 285 \]

### Step 6: Solve for \( x \)
To find \( x \), multiply both sides by 3:
\[ 19x = 285 \times 3 \]
Calculating the right side:
\[ 19x = 855 \]
Now, divide by 19:
\[ x = \frac{855}{19} = 45 \]

### Step 7: Find the Runs Scored by Sachin
Now that we have \( x \), we can find the number of runs scored by Sachin:
\[ S = 3x = 3 \times 45 = 135 \]

### Final Answer
Thus, the number of runs scored by Sachin in that match is **135**.

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