Furniture Price Ratio Calculation
The problem asks for the price of the cheapest furniture item given the average price of three items and the ratio of their prices.
Calculating Total Price
First, find the total price of the three furniture items.
- Average Price = ₹16,005
- Number of Items = 3
- Total Price = Average Price × Number of Items
- Total Price = $16,005 \times 3 = ₹48,015$
Using Price Ratio
The prices are in the ratio 3 : 5 : 7. Let the prices be $3x$, $5x$, and $7x$, where $x$ is a common multiplier.
- The sum of the ratio parts is $3 + 5 + 7 = 15$.
- The sum of the actual prices is $3x + 5x + 7x = 15x$.
Solving for the Multiplier
Equate the sum of the actual prices to the total price calculated earlier.
- $15x = ₹48,015$
- $x = \frac{₹48,015}{15}$
- $x = ₹3,201$
Finding the Cheapest Price
The cheapest item corresponds to the smallest part of the ratio, which is 3.
- Price of Cheapest Item = $3x$
- Price of Cheapest Item = $3 \times ₹3,201$
- Price of Cheapest Item = ₹9,603
Therefore, the price of the cheapest item is ₹9,603.
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