The ratio of work efficiency of A & B is 2:5 . If A & B . If A & B work together and completed a piece of work in 30 days , In how many days the work is completed when A works alone ?

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Efficiency Ratio
The efficiency ratio of A and B is given as 2:5. This means:
- Efficiency of A (E_A) = 2 units of work per day
- Efficiency of B (E_B) = 5 units of work per day

### Step 2: Calculate Total Efficiency
When A and B work together, their combined efficiency is:
\[ E_{total} = E_A + E_B = 2 + 5 = 7 \text{ units of work per day} \]

### Step 3: Calculate Total Work
It is given that A and B together complete the work in 30 days. Therefore, the total work (TW) can be calculated as:
\[ TW = E_{total} \times \text{Number of days} = 7 \times 30 = 210 \text{ units of work} \]

### Step 4: Calculate A's Work Rate
Now, we need to find out how many days A would take to complete the same amount of work alone. Since A's efficiency is 2 units of work per day, we can calculate the time taken by A (T_A) to complete the total work:
\[ T_A = \frac{TW}{E_A} = \frac{210}{2} = 105 \text{ days} \]

### Final Answer
If A works alone, it will take him **105 days** to complete the work.

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