Question

The total share of A,B and C is 669 in such a way that the ratio of the shares of A and B is 17:27 and that of B and C is 2:5. What is the share of C?

• A. 405
• B. 135
• C. 270
• D. 223

Answer 1

The Correct Option is A

Finding the Share of C 

Given Ratios:

• \( A : B = 17 : 27 \)
• \( B : C = 2 : 5 \)

Step 1: Express \( B \) in a Common Term

To find a common term for \( B \), we determine the LCM of 27 and 2:

\[ \text{LCM}(27, 2) = 54 \]

Step 2: Adjust the Ratios

• Multiply the first ratio by 2: \[ A : B = (17 \times 2) : (27 \times 2) = 34 : 54 \]
• Multiply the second ratio by 27: \[ B : C = (2 \times 27) : (5 \times 27) = 54 : 135 \]

Step 3: Combine the Ratios

Now, combining both adjusted ratios:

\[ A : B : C = 34 : 54 : 135 \]

Step 4: Solve for \( x \)

Given that the total sum is 669, we set up the equation:

\[ 34x + 54x + 135x = 669 \]

\[ 223x = 669 \]

Solving for \( x \):

\[ x = \frac{669}{223} = 3 \]

Step 5: Find the Share of \( C \)

\[ C = 135 \times 3 = 405 \]

Final Answer:

Thus, the share of C is 405 (Option A).