A and B working together can complete a job in 30 days. The ratio of their efficiencies is 3 : 2. In how many days can the faster person complete the job?

Options

A. 50
B. 30
C. 40
D. 60

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the given information
A and B can complete a job together in 30 days, and the ratio of their efficiencies is 3:2.

### Step 2: Calculate the total work
Since A and B together complete the job in 30 days, we can express the total work in terms of their combined efficiencies.

Let the total work be represented in units. If A's efficiency is 3 units/day and B's efficiency is 2 units/day, then their combined efficiency is:
\[ 3 + 2 = 5 \text{ units/day} \]

Now, the total work done in 30 days is:
\[ \text{Total Work} = \text{Efficiency} \times \text{Time} \]
\[ \text{Total Work} = 5 \text{ units/day} \times 30 \text{ days} = 150 \text{ units} \]

### Step 3: Determine A's efficiency
From the ratio of efficiencies (3:2), we know that A's efficiency is 3 units/day.

### Step 4: Calculate the time taken by A to complete the job alone
To find out how many days A will take to complete the job alone, we can use the formula:
\[ \text{Time} = \frac{\text{Total Work}}{\text{Efficiency of A}} \]
Substituting the values we have:
\[ \text{Time} = \frac{150 \text{ units}}{3 \text{ units/day}} = 50 \text{ days} \]

### Conclusion
Thus, the faster person (A) can complete the job in **50 days**.

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