The ratio of working efficiency of A and B is 5:3 and the ratio of efficiency of B and C is 5:8. Who is the most efficient?

Options

A. A
B. B
C. C
D. can't be determined

Answer

To solve the problem, we need to compare the efficiencies of A, B, and C based on the given ratios.

### Step-by-Step Solution:

1. **Understand the Ratios Given:**
- The ratio of the working efficiency of A and B is given as \( A : B = 5 : 3 \).
- The ratio of the efficiency of B and C is given as \( B : C = 5 : 8 \).

2. **Express Efficiencies in Terms of a Common Variable:**
- Let the efficiency of A be \( 5x \) and the efficiency of B be \( 3x \) (from the first ratio).
- From the second ratio \( B : C = 5 : 8 \), we can express B in terms of C. If we let the efficiency of B be \( 5y \) and C be \( 8y \).

3. **Equate the Efficiencies of B:**
- From the two expressions for B, we have:
\[ 3x = 5y \]
- This can be rearranged to find a relationship between \( x \) and \( y \):
\[ y = \frac{3x}{5} \]

4. **Substitute y to Find C's Efficiency:**
- Now substitute \( y \) back into the expression for C:
\[ C = 8y = 8 \left(\frac{3x}{5}\right) = \frac{24x}{5} \]

5. **Summarize the Efficiencies:**
- Now we have the efficiencies expressed in terms of \( x \):
- Efficiency of A: \( 5x \)
- Efficiency of B: \( 3x \)
- Efficiency of C: \( \frac{24x}{5} \)

6. **Compare the Efficiencies:**
- To compare, we can convert all efficiencies to a common denominator:
- Efficiency of A: \( 5x = \frac{25x}{5} \)
- Efficiency of B: \( 3x = \frac{15x}{5} \)
- Efficiency of C: \( \frac{24x}{5} \)

7. **Determine the Most Efficient:**
- Comparing \( \frac{25x}{5} \), \( \frac{15x}{5} \), and \( \frac{24x}{5} \):
- A: \( 25x/5 \)
- B: \( 15x/5 \)
- C: \( 24x/5 \)
- Clearly, \( 25x/5 > 24x/5 > 15x/5 \).

8. **Conclusion:**
- Therefore, A is the most efficient.

### Final Answer:
A is the most efficient.

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