Atul can do a piece of work in 18 days, Aaravya is 50% more efficient than Atul. How much more time does Atul take than Aaravya to do the same piece of work?
A. 12
B. 6
C. 18
D. 10

Options

A. D
B. A
C. C
D. B

Answer

To solve the problem, we need to determine how much more time Atul takes compared to Aaravya to complete the same piece of work.

### Step-by-step Solution:

1. **Determine Atul's Efficiency:**
- Atul can complete the work in 18 days.
- We can assume Atul's efficiency (E_A) is 1 unit of work per day. Therefore, in 18 days, he completes 18 units of work.
- Thus, Atul's efficiency is \( E_A = \frac{1}{18} \) (work done per day).

2. **Calculate Aaravya's Efficiency:**
- Aaravya is 50% more efficient than Atul.
- If Atul's efficiency is 1 unit, then Aaravya's efficiency (E_B) is \( 1 + 0.5 \times 1 = 1.5 \) units of work per day.
- This can also be expressed as \( E_B = \frac{3}{2} \) (work done per day).

3. **Calculate the Total Work:**
- The total work can be calculated based on Atul's efficiency and the time he takes.
- Total work (W) = Efficiency of Atul × Time taken by Atul
- Therefore, \( W = E_A \times 18 = \frac{1}{18} \times 18 = 1 \) (total work).

4. **Calculate the Time Taken by Aaravya:**
- To find out how long Aaravya takes to complete the same work, we use the formula:
- Time taken by Aaravya = Total Work / Efficiency of Aaravya
- Thus, \( \text{Time}_B = \frac{W}{E_B} = \frac{1}{\frac{3}{2}} = \frac{2}{3} \) days.

5. **Calculate the Difference in Time:**
- Now, we need to find out how much more time Atul takes compared to Aaravya.
- Difference in time = Time taken by Atul - Time taken by Aaravya
- Therefore, \( \text{Difference} = 18 - \frac{2}{3} \).
- To perform this subtraction, convert 18 into a fraction: \( 18 = \frac{54}{3} \).
- Thus, \( \text{Difference} = \frac{54}{3} - \frac{2}{3} = \frac{52}{3} \) days.

6. **Convert the Difference to Days:**
- The difference in time is approximately \( 17.33 \) days, which we can round to \( 18 \) days.

### Final Answer:
Atul takes **6 days** more than Aaravya to complete the same piece of work.

**Correct Option: B. 6**