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The average price of three items of furniture is Rs 16800. If their prices are in the ratio 3:5:7, the price of the cheapest item (in Rs) is
3360
7840
5600
10080
10080
Calculate the sum of prices first: 16800├Ч3=50400. Sum the ratio parts: 3+5+7=15. Find the value of one part: 50400/15=3360. The cheapest item is 3├Ч3360=10080.
Average price of three items is Rs 16800. The ratio of prices is 3:5:7.
Average=nSumтАЛ, PriceitemтАЛ=RatiopartтАЛ├Чx
Calculate the sum of prices first: 16800├Ч3=50400. Sum the ratio parts: 3+5+7=15. Find the value of one part: 50400/15=3360. The cheapest item is 3├Ч3360=10080.
Many students confuse 'cheapest item' with 'the first ratio value', or incorrectly calculate the sum as 16800/3 instead of 16800├Ч3.
Calculate Total Price
Since the average of 3 items is 16800, the total price is the average multiplied by 3.
Total=16800├Ч3=50400
Sum the Ratio Parts
The prices are in ratio 3:5:7. Let the items be 3x, 5x, and 7x. The sum of parts is 3 + 5 + 7 = 15.
Sum┬аof┬аparts=15x
Solve for x
Equate the sum of parts to the total price to find the value of one part.
15x=50400тЯ╣x=1550400тАЛ=3360
Find Cheapest Price
The cheapest item corresponds to the smallest ratio part, which is 3.
PricecheapestтАЛ=3├Ч3360=10080
D is correct because the total sum of prices is 50400, leading to a unit value of 3360, making the cheapest item 3 ├Ч 3360 = 10080.
This concept of 'Value per Unit' in ratios is fundamental for Partnership and Profit & Loss problems in competitive exams.
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