The value of a concept coin is inversely proportional to its radius.

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

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.

value of CC is inversely proportional to radius; radius reduced to 1/4 will increase value by 4 times that is 400% IMO A

The initial area for the coin is pi*r^2. if the radius is 4 initially, the initial area was 16pi. If the coin is melted and used to form multiple coins we need to know how many coins were formed .The radius of the new coin is 1/4th that of the original.So it's area is in this case pi*1^2 which is just pi.The ratio of the two areas is 16:1 meaning 16 coins of radius 1/4th of the original can be formed. The value of each of the coins is k/1.The value of the 16 coins is 16k. The value of the original coin is k/4. The change would be (16k-k/4)/(k/4) . the answer will be 63 and when multiplied by 100 will be 6300%.The answer is thus D

initial r = 16 so area = pi * 16^2
later 1/4th r = 4 area ; pi * 4^2
we have % increase ; 256pi-16pi/16pi = 1500%
IMO B

Let radius be r and height be h initially

Old volume of the coin = pi.r^2.h
Since, value is inversely proportional to radius.
If radius is reduced to 1/4th,
Therefore, Volume of one coin = pi.(1/4r)^2.h = 1/16.pi.r^2.h
Thus, bigger coin is melted into 16 such coins.
Since, value is inversely proportional to radius.
And radius is reduced by 1/4, value will be increased by 4 times for one coin ie 4V1.
Since, there are 16 such coins, value for 16 coins would be 16*4*V1 =64V1.

Therefore %increase in value for new coins would be (64-1)v1/v1*100% = 6300%

Answer is D.

Posted from my mobile device

Hello,

You seem to be misunderstanding something; the square of radius is being used only to find the number of new coins casted.

Please watch the video explanation carefully, especially the last ~40 secs.



All the best!
Experts'Global team
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Let Value of 1 coin initially be V and its radius be r,
Value of new coin Vn

The value of a concept coin is inversely proportional to its radius, so

V \(\alpha\) 1/r

New radius is r/4 , so

New Vn \(\alpha\) 1/(r/4)

=> Vn \(\alpha\) 4/r

=> Vn \(\alpha\) 4* 1/r

i.e. Value of new 1 coin is 4 times the initial Value --- (1)

Now , we need to find total no of new coins created

Old coin area = \(\pi\) r^2 .h

Area of new coin = \(\pi\) (r/4)^2 .h = \(\pi\) r^2/16 .h

No of new coins created = Area of old coin / Area of new coin = (\(\pi\) r^2 .h ) / ( \(\pi\) r^2/16 .h) =16

By (1 ) , Value of 1 coin is 4 times initial value
=> Value of 16 new coins = 4 * 16 =64

% Value increase = (New - Old ) *100 /Old = (64-1) *100 /1 = 6300 %

***Please correct if any mistake in above, this is my first post !

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