To do a certain work, the ratio of the efficiencies of A and B is 7 : 5. Working together, they can complete the same work in `17(1)/(2)` days. A alone will complete 60% of the same work in:

Options

A. 21 days
B. 16 days
C. 15 days
D. 18 days

Answer

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

### Step 1: Understand the given information
We know that the ratio of efficiencies of A and B is 7:5. This means if A's efficiency is 7 units of work per day, then B's efficiency is 5 units of work per day.

### Step 2: Calculate the combined efficiency of A and B
To find the combined efficiency of A and B, we add their efficiencies:
\[ \text{Combined Efficiency} = 7 + 5 = 12 \text{ units of work per day} \]

### Step 3: Calculate the total work done
We are given that A and B together can complete the work in \(17\frac{1}{2}\) days. First, convert \(17\frac{1}{2}\) days into an improper fraction:
\[ 17\frac{1}{2} = \frac{35}{2} \text{ days} \]
Now, we can calculate the total work using the formula:
\[ \text{Total Work} = \text{Combined Efficiency} \times \text{Time} \]
Substituting the values we have:
\[ \text{Total Work} = 12 \times \frac{35}{2} = 12 \times 17.5 = 210 \text{ units of work} \]

### Step 4: Calculate the work A will do alone
We need to find out how long A will take to complete 60% of the total work. First, calculate 60% of the total work:
\[ 60\% \text{ of Total Work} = \frac{60}{100} \times 210 = 126 \text{ units of work} \]

### Step 5: Calculate the time taken by A to complete 126 units of work
Since A's efficiency is 7 units of work per day, we can find the time taken by A to complete 126 units of work using the formula:
\[ \text{Time} = \frac{\text{Work}}{\text{Efficiency}} \]
Substituting the values:
\[ \text{Time} = \frac{126}{7} = 18 \text{ days} \]

### Final Answer
A alone will complete 60% of the same work in **18 days**.

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