The efficiencies of A, B and C are in the ratio of 2: 3: 5. Working together, they can complete a task in 6 days. In how many days will A alone complete 20% of that task?

Options

A. 8
B. 5
C. 6
D. 4

Answer

To solve the problem step by step, we will follow the given information about the efficiencies of A, B, and C, and how they work together.

### Step 1: Determine the efficiencies of A, B, and C
The efficiencies of A, B, and C are given in the ratio of 2:3:5. This means:
- Efficiency of A = 2x
- Efficiency of B = 3x
- Efficiency of C = 5x

### Step 2: Calculate the total efficiency when A, B, and C work together
To find the total efficiency, we add the individual efficiencies:
Total efficiency = Efficiency of A + Efficiency of B + Efficiency of C
= 2x + 3x + 5x = 10x

### Step 3: Determine the total work done
It is given that A, B, and C together can complete the task in 6 days. Therefore, the total work can be calculated as:
Total Work = Total Efficiency × Number of Days
= 10x × 6 = 60x

### Step 4: Calculate the total work in terms of units
Since we have established that the total work is 60x, we can set x = 1 for simplicity. Thus, the total work = 60 units.

### Step 5: Calculate 20% of the total work
Now, we need to find out how much work corresponds to 20% of the total work:
20% of Total Work = 20/100 × 60 = 12 units

### Step 6: Determine how long A will take to complete 12 units of work
A's efficiency is 2x. Since we set x = 1, A's efficiency = 2 units/day. To find out how many days A will take to complete 12 units of work, we use the formula:
Days = Work / Efficiency
= 12 units / 2 units/day = 6 days

### Final Answer
A alone will complete 20% of the task in **6 days**.

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