When A, B and C are deployed for a task, A and B together do `70%` of 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 step by step, we will analyze the work done by A, B, and C based on the information provided.

### Step 1: Understand the total work done
The total work is considered to be 100%.

### Step 2: Calculate the work done by C
From the first piece of information, A and B together do 70% of the work. Therefore, the remaining work done by C can be calculated as:
\[ \text{Work done by C} = 100\% - 70\% = 30\% \]

### Step 3: Calculate the work done by A
From the second piece of information, B and C together do 50% of the work. Therefore, the remaining work done by A can be calculated as:
\[ \text{Work done by A} = 100\% - 50\% = 50\% \]

### Step 4: Calculate the work done by B
Now we can find out how much work B has done. We know:
- A has done 50%
- C has done 30%
- A and B together did 70% of the work.

We can set up the equation:
\[ \text{Work done by A} + \text{Work done by B} = 70\% \]
Substituting A's work:
\[ 50\% + \text{Work done by B} = 70\% \]
Solving for B:
\[ \text{Work done by B} = 70\% - 50\% = 20\% \]

### Step 5: Summarize the work done by each person
Now we have:
- Work done by A = 50%
- Work done by B = 20%
- Work done by C = 30%

### Step 6: Determine the most efficient worker
Since efficiency is directly proportional to the amount of work done, we can conclude:
- A is the most efficient as A has done 50% of the work.

### Conclusion
Thus, the answer to the question is that A is the most efficient worker.

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