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The average price of three items of furniture is Rs 16440. If their prices are in the ratio 3:5:7, the price of the cheapest item (in Rs) is
9864
3288
5480
7672
9864
Calculate the sum of ratios (3+5+7=15). The average of ratios is 15/3=5. Equate the ratio average to the given average: 5x=16440. Then, the cheapest item is 3x=(16440/5)├Ч3.
Average price of 3 items = Rs 16440. Ratio of prices = 3:5:7.
Average=nтИСValuesтАЛ
Calculate the sum of ratios (3+5+7=15). The average of ratios is 15/3=5. Equate the ratio average to the given average: 5x=16440. Then, the cheapest item is 3x=(16440/5)├Ч3.
Students often calculate 16440├Ч3=49320 as the sum and then divide by 15, but they may misinterpret 'cheapest item' as 3, 5, or 7 instead of the value 3x.
Calculate Total Price
Since the average price of 3 items is Rs 16440, the total price is the average multiplied by 3.
Total=16440├Ч3=49320
Assign Algebraic Variables
Using the ratio 3:5:7, let the prices be 3x, 5x, and 7x.
3x+5x+7x=15x
Solve for x
Equate the sum of ratios to the total price to find the value of one part x.
15x=49320тЯ╣x=1549320тАЛ=3288
Find the Cheapest Item
The cheapest item corresponds to the smallest ratio value, which is 3x.
3├Ч3288=9864
A is correct because the total sum of prices is 49320, which results in x=3288 and the cheapest item 3x=9864.
This ratio-summation method is identical to the method used in 'Partnership' and 'Mixture & Allegation' problems.
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