The average price of three items of furniture is Rs. 15000. If the prices of the items are in the ratio 3 : 5 : 7, what is the price of the cheapest item of furniture?

Introduction / Context:
This problem tests the use of ratios along with the concept of average value. Such questions are common in aptitude tests to see whether a candidate can connect average, total value and ratio distribution.

Given Data / Assumptions:
- Average price of three furniture items = Rs. 15000.
- Prices are in the ratio 3 : 5 : 7.
- We assume prices are positive and there are exactly three items.

Concept / Approach:
If three items have prices in the ratio 3 : 5 : 7, we can represent them as 3x, 5x and 7x. The average price is then:
Average price = (3x + 5x + 7x) / 3
We equate this to Rs. 15000 to find the value of x, and then compute the individual prices. The cheapest item corresponds to the smallest term in the ratio.

Step-by-Step Solution:
Step 1: Let the three prices be 3x, 5x and 7x.Step 2: Total price = 3x + 5x + 7x = 15x.Step 3: Average price = (Total price) / 3 = 15x / 3 = 5x.Step 4: Given average price = Rs. 15000, so 5x = 15000.Step 5: Solve for x: x = 15000 / 5 = 3000.Step 6: Cheapest item price = 3x = 3 * 3000 = Rs. 9000.

Verification / Alternative check:
You can also find the total directly from the average: Total = 3 * 15000 = Rs. 45000. Splitting Rs. 45000 in the ratio 3 : 5 : 7 means the unit value is 45000 / 15 = 3000. Thus, the three prices are 9000, 15000 and 21000, and the smallest is 9000, confirming the result.

Why Other Options Are Wrong:
- 6000: This would correspond to 2x with x = 3000 and does not match the given ratio structure.
- 7000: This is not a multiple of the base unit 3000, so it does not satisfy the ratio 3 : 5 : 7.
- 8888: This is an arbitrary number and does not align with the derived unit value or the ratio.

Common Pitfalls:
- Some learners mistakenly divide the average by the ratio parts without computing the total first.
- Others assign x directly as 15000, ignoring that the ratio is spread across three items and that the average equals only 5x, not x.

Final Answer:
The price of the cheapest furniture item is Rs. 9000.