A is 30% more efficient than B. If B finishes a work in 13 days, then in how many days will A finish the same work?

Options

A. 11
B. 9
C. 10
D. 12

Answer

To solve the problem step by step, we will first determine the efficiency of A and B, and then calculate how many days A will take to finish the work.

### Step 1: Understand the efficiency relationship
A is 30% more efficient than B. This means if B's efficiency is considered as 100%, then A's efficiency will be:
\[ \text{Efficiency of A} = 100\% + 30\% = 130\% \]

### Step 2: Convert efficiencies to a ratio
We can express the efficiencies in a ratio:
- Efficiency of B = 100 (let's assume B's efficiency is 100 units of work per day)
- Efficiency of A = 130 (A's efficiency is 130 units of work per day)

### Step 3: Determine the work done by B
If B finishes the work in 13 days, we can calculate the total work done:
\[ \text{Total Work} = \text{Efficiency of B} \times \text{Time taken by B} = 100 \times 13 = 1300 \text{ units of work} \]

### Step 4: Calculate the time taken by A
Now, we can find out how many days A will take to finish the same work. Since A's efficiency is 130 units of work per day, we can use the formula:
\[ \text{Time taken by A} = \frac{\text{Total Work}}{\text{Efficiency of A}} = \frac{1300}{130} = 10 \text{ days} \]

### Final Answer
A will finish the work in **10 days**.

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