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The average price of three items of furniture is Rs 16890. If their prices are in the ratio 3:5:7, the price of the cheapest item (in Rs) is
10134
3378
5630
7882
10134
Calculate the sum of ratios (3+5+7=15). Divide the total price (16890├Ч3) by the sum of ratios (15) to get the value of one part (x=3378). The cheapest item corresponds to 3 parts.
Average price of 3 items = Rs 16890, Ratio of prices = 3:5:7
Average=nтИСItemsтАЛ, PricecheapestтАЛ=RatiominтАЛ├Чx
Calculate the sum of ratios (3+5+7=15). Divide the total price (16890├Ч3) by the sum of ratios (15) to get the value of one part (x=3378). The cheapest item corresponds to 3 parts.
Students often divide the average price (16890) directly by the sum of ratios (15) instead of the total price (16890 ├Ч 3 = 50670), leading to an incorrect result.
Calculate Total Price
Since the average of 3 items is 16890, the total price is the average multiplied by the number of items.
Total=16890├Ч3=50670
Determine Ratio Parts
Sum the given ratio parts: 3x+5x+7x=15x. Equate this to the total sum.
15x=50670
Find Value of one unit
Divide the total price by the sum of the ratio parts to find the value of x.
x=1550670тАЛ=3378
Calculate Cheapest Item
The cheapest item is represented by the smallest ratio part, which is 3.
3x=3├Ч3378=10134
A is correct because the total sum of prices is 50670, dividing by the 15 ratio units gives 3378 per unit, and 3 units equal 10134.
This ratio-sum method is highly effective for 'Mixture and Alligation' problems and 'Partnership' profit distribution questions.
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