A can complete a piece of work working along with B in 20 days. If he can complete the same work working along with C in 10 days, then between B and C who is more efficient ?

Answer

To solve the problem step by step, we will determine the efficiencies of A, B, and C based on the information provided.

### Step-by-Step Solution:

**Step 1: Determine the total work done.**
Assume the total work is 20 units (this is a convenient number based on the days given).

**Hint for Step 1:** Start by assuming a total work amount that makes calculations easier, such as 20 units.

**Step 2: Calculate the efficiency of A and B together.**
Since A and B can complete the work in 20 days:
- Efficiency of A + B = Total Work / Days = 20 units / 20 days = 1 unit per day.

**Hint for Step 2:** Use the formula: Efficiency = Total Work / Time taken to find how much work is done together.

**Step 3: Calculate the efficiency of A and C together.**
Since A and C can complete the work in 10 days:
- Efficiency of A + C = Total Work / Days = 20 units / 10 days = 2 units per day.

**Hint for Step 3:** Again, apply the same formula to find the combined efficiency of A and C.

**Step 4: Determine A's efficiency.**
Let A's efficiency be 'a', B's efficiency be 'b', and C's efficiency be 'c'.
From the previous steps:
- A + B = 1 unit/day (Equation 1)
- A + C = 2 units/day (Equation 2)

**Hint for Step 4:** Use variables to represent the efficiencies of A, B, and C for easier calculations.

**Step 5: Solve for A's efficiency using the equations.**
From Equation 1:
- A + B = 1
- Therefore, B = 1 - A (Equation 3)

From Equation 2:
- A + C = 2
- Therefore, C = 2 - A (Equation 4)

**Hint for Step 5:** Rearrange the equations to express B and C in terms of A.

**Step 6: Substitute A's efficiency to find B and C.**
We know from the equations:
- If we assume A's efficiency is 'a', we can substitute 'a' into Equations 3 and 4 to find B and C.

**Step 7: Compare the efficiencies of B and C.**
- From Equation 3: B = 1 - a
- From Equation 4: C = 2 - a

To find out who is more efficient, we compare B and C:
- If C > B, then C is more efficient.
- If 2 - a > 1 - a, then C is more efficient.

**Step 8: Simplify the comparison.**
- Simplifying gives us: 2 - a > 1 - a
- This simplifies to: 2 > 1, which is always true.

**Conclusion:**
C is more efficient than B.

**Final Answer:** C is more efficient than B.