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18 Jun 2019, 00:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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28% (02:27) correct
72%
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based on 271
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The value of a concept coin is inversely proportional to its radius. If a coin was melted and smaller coins with radii 1/4th of the original coin and thickness same as that of the original coin were made(using all the metal of the original coin), what will the overall percentage increase in value after the operation?
A. 400%
B. 1500%
C. 1600%
D. 6300%
E. 6400%
A. 400%
B. 1500%
C. 1600%
D. 6300%
E. 6400%
19 Jun 2019, 06:34
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Bunuel
Let the radius of original coin = r
Small coins of radius r/4 are formed from original coin with same thickness.
Let n be the number of small coins that are formed
--> pi*\(r^2\) = n*pi*\((r/4)^2\)
--> pi*\(r^2\) = n*pi*\(r^2\)/16
--> n = 16
So, 16 such smaller coins have formed from original coin.
value of a concept coin is inversely proportional to its radius
--> value (v) ∝ 1/r
--> v = k*1/r, where k is any constant
--> v*r = k
--> \(v_1\)*\(r_1\) = \(v_2\)*\(r_2\)
Given, \(r_2\) = \(r_1\)/4 = \(r/4\)
Assume initial value, \(v_1\) = 100
--> 100*\(r\) = \(v_2\)*\(r\)/4
--> \(v_2\) = 400
Value of 1 small coin = 400
--> Value of 16 such coins = 16*400 = 6400
% increase in value = \(\frac{(Final - Initial)}{Initial}\)*\(100\)
= \(\frac{(6400 - 100)}{100}\)*\(100\)
= \(\frac{6300}{100}\)*\(100\)
= \(6300\) %
IMO Option D
Pls Hit Kudos if you like the solution
18 Jun 2019, 17:55
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This problem contains an error.
At first statement, the problem says that value is proportional to radius. But in all preceding explanations, value is proportional to square of radius.
Please correct me if I am wrong.
At first statement, the problem says that value is proportional to radius. But in all preceding explanations, value is proportional to square of radius.
Please correct me if I am wrong.
