if a does 33 by 1/3 % of the work in 17 days then in how many days whole work will be completed

To solve this problem, we need to determine how long it would take for \( A \) to complete the entire work based on the given information.

### Step 1: Determine the fraction of work done by \( A \).
- \( A \) completes \( \frac{1}{3} \% \) of the work in 17 days.
- \( \frac{1}{3} \% \) can be written as \( \frac{1}{3 \times 100} = \frac{1}{300} \).

This means \( A \) does \( \frac{1}{300} \) of the total work in 17 days.

### Step 2: Determine the work rate of \( A \).
- Work rate \( R \) is given by work done per day.
- \( R = \frac{\text{Work done}}{\text{Time taken}} = \frac{\frac{1}{300}}{17} = \frac{1}{300 \times 17} \).

### Step 3: Calculate the time required to complete the whole work.
- To complete the whole work, \( A \) would need \( T \) days, where:
\[ T = \frac{\text{Total Work}}{\text{Work rate}} = \frac{1}{\frac{1}{300 \times 17}} = 300 \times 17 = 5100 \text{ days} \]

So, \( A \) would take **5100 days** to complete the whole work.

Would you like any further details or explanations?

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Here are 8 related questions for practice:

1. If \( B \) does 25% of the work in 20 days, how long will \( B \) take to complete the whole work?
2. What is the work rate of a person who completes 10% of a task in 5 days?
3. If \( C \) can complete the entire work in 30 days, how much work does \( C \) complete in 10 days?
4. Two people can complete a task together in 15 days. If one person works twice as fast as the other, how long would each take to complete the work alone?
5. If a task is 60% complete and 12 days have passed, how long will it take to finish the remaining work at the same rate?
6. How would the time change if \( A \) worked 10% faster on the same task?
7. If the work rate doubles, how many days will it take to complete a task that originally took 20 days?
8. What fraction of the work is done after 25 days if a person completes the work in 100 days?

**Tip:** When dealing with work problems, it’s often useful to express rates as fractions of the whole task and to set up equations that relate these rates to time.

Learn how to calculate the time required to complete a work based on given completion rates. This example problem involves determining how long it would take for someone to complete the entire work if they complete a fraction of it in a specified time. Suitable for Grades 7-9 students studying percentages and work-time problems.

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