3. The price of gold is directly
proportional to square of its weight.
A person broke down the gold in the
ratio of 3 : 2 : 1 and faces a loss of
* 4620. Find the initial price of gold.
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The price of a gold nugget is directly proportional to the square of its weight. If a person breaks down the gold nugget in the ratio of 3:2:1 and gets a loss of Rs. 4620, what is the initial price of the gold nugget?
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7560 Rs.
We are given that the price of gold is directly proportional to square of its weight.
=> Price = k*weight^2
Let us say initially the weight of the nugget was 6 units
=> P(original) = k*6^2 = 36k
After breaking it down into three pieces, we get the weights as 3, 2, and 1
=> P(3) = k*3^2 = 9k
=> P(2) = k*2^2 = 4k
=> P(1) = k*1^2 = k
=> P(new) = 9k + 4k + k = 14k
Loss = 36k - 14k = 4620 Rs.
=> 22k = 4620 Rs.
=> k = 210
=> Price (original) = 210*36 = 7560 Rs.
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