When A, B and Care deployed for a task, A and B together do `70%` of the work and B and C together do `50%` of the work. Who is most efficient?

Options

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

Answer

To solve the problem, we need to analyze the work done by A, B, and C based on the information provided. Here’s a step-by-step breakdown of the solution:

### Step 1: Define Total Work
Assume the total work to be 100%.

### Step 2: Work Done by A and B
According to the problem, A and B together do 70% of the work.
So,
\[ A + B = 70\% \]

### Step 3: Work Done by B and C
It is also given that B and C together do 50% of the work.
So,
\[ B + C = 50\% \]

### Step 4: Calculate Work Done by C
To find the work done by C, we can use the total work:
\[ C = 100\% - (A + B) = 100\% - 70\% = 30\% \]

### Step 5: Calculate Work Done by B
Now that we know C's work, we can find B's work using the equation from Step 3:
\[ B + C = 50\% \]
Substituting C's value:
\[ B + 30\% = 50\% \]
Thus,
\[ B = 50\% - 30\% = 20\% \]

### Step 6: Calculate Work Done by A
Finally, we can find A's work using the equation from Step 2:
\[ A + B = 70\% \]
Substituting B's value:
\[ A + 20\% = 70\% \]
Thus,
\[ A = 70\% - 20\% = 50\% \]

### Step 7: Compare Work Done
Now we have:
- A's work = 50%
- B's work = 20%
- C's work = 30%

### Step 8: Determine the Most Efficient Worker
To determine who is the most efficient, we compare the work done:
- A has done the most work (50%), followed by C (30%), and then B (20%).

### Conclusion
Thus, the most efficient worker is **A**.