In an innings of a cricket match, three players A, B and C scored a total of 361 runs. If the ratio of the number of runs scored by A to that scored by B and also number of runs scored by B to that scored by C be `3 : 2`, the number of runs scored by A was

Options

A. 171
B. 181
C. 185
D. 161

Answer

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

### Step 1: Understand the Ratios
We are given that the ratio of runs scored by A to B is 3:2, and the ratio of runs scored by B to C is also 3:2.

### Step 2: Express the Ratios in Terms of a Common Variable
Let the runs scored by A, B, and C be represented as:
- A = 3x
- B = 2x (from the ratio A:B)
- C = (2/3) * B = (2/3) * (2x) = (4/3)x (from the ratio B:C)

### Step 3: Set Up the Equation
Now, we know that the total runs scored by A, B, and C is 361. Therefore, we can write the equation:
\[ A + B + C = 361 \]
Substituting the values we have:
\[ 3x + 2x + \frac{4}{3}x = 361 \]

### Step 4: Combine the Terms
To combine the terms, we need a common denominator. The common denominator for 1 and 3 is 3. Thus, we rewrite the equation:
\[ 3x + 2x + \frac{4}{3}x = \frac{9x}{3} + \frac{6x}{3} + \frac{4x}{3} = \frac{19x}{3} \]

### Step 5: Solve for x
Now, we set the equation:
\[ \frac{19x}{3} = 361 \]
To eliminate the fraction, multiply both sides by 3:
\[ 19x = 361 \times 3 \]
\[ 19x = 1083 \]
Now, divide both sides by 19:
\[ x = \frac{1083}{19} = 57 \]

### Step 6: Calculate the Runs Scored by A
Now that we have the value of x, we can find the runs scored by A:
\[ A = 3x = 3 \times 57 = 171 \]

### Conclusion
The number of runs scored by A is **171**.

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