The ratios of efficiencies of A and B of doing a certain work is 5 : 8. Working together they can complete the work in 20 days, A alone will complete 25% of that work in:

Options

A. 14 days
B. 12 days
C. 11 days
D. 13 days

Answer

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

### Step 1: Understand the Efficiency Ratio
The efficiencies of A and B are given in the ratio of 5:8. This means that for every 5 units of work A can do, B can do 8 units of work.

### Step 2: Calculate Total Efficiency
To find the total efficiency when A and B work together, we add their efficiencies:
- Efficiency of A = 5 units
- Efficiency of B = 8 units
- Total Efficiency (A + B) = 5 + 8 = 13 units

### Step 3: Calculate Total Work Done
It is given that A and B together can complete the work in 20 days. Therefore, the total work can be calculated as:
- Total Work = Total Efficiency × Number of Days
- Total Work = 13 units/day × 20 days = 260 units

### Step 4: Calculate A's Contribution to the Total Work
Since A's efficiency is 5 units, we can find out how much work A does in total:
- Work done by A = (A's Efficiency / Total Efficiency) × Total Work
- Work done by A = (5/13) × 260 = 100 units

### Step 5: Calculate Work Done by A in 25% of Total Work
We need to find out how much time A takes to complete 25% of the total work:
- 25% of Total Work = 25/100 × 260 = 65 units

### Step 6: Calculate Days Taken by A to Complete 65 Units
Now we will find out how many days A will take to complete 65 units of work:
- Days taken by A = Work to be done by A / A's Efficiency
- Days taken by A = 65 units / 5 units/day = 13 days

### Final Answer
A alone will complete 25% of that work in **13 days**.

---