If Juanita gives half of her bitcoins in a 1: 2 ratio to Pat and Svetl

If Juanita gives half of her bitcoins in a 1: 2 ratio to Pat and Svetlana, respectively, then Pat will have one fourth as many bitcoins as will Svetlana, who will in turn have twice as many bitcoins as will Juanita. If Pat currently has 2 bitcoins, then how many more bitcoins does Juanita currently have than Svetlana?


A. 8

B. 12

C. 20

D. 22

E. 24

Explanation: Let Juanita has J coins then Juanita will give half of her bitcoins(i.e J/2 coins) in a 1: 2 ratio (i.e J/6 :J/3 coins) to Pat and Svetlana
means Pat will have =P+J/6 coins and Svetlana will have=S+J/3 coins

given Pat has currently 2 coins i.e P=2
and P+J/6=1/4(S+J/3) & S+J/3=2*J/2
2+J/6=1/4(S+J/3) & S+J/3=2*J/2
S/4-J/12=2 & S=2J/3
J/6-J/12=2
J=24

So J-S=24-16
=8

Hence A is the correct answer.

Pat Originally has 2 Bitcoins.


Let Junita have 6x coins. Half of that is 3x, which in a 1:3 ratio is x and 2x given to Pat and Svetlana respectively.

So after the distribution, Junita has 3x coins....(1)


After the distribution

Pat has 2 + x coins, which is 1/4 th of what Svetlana has.

So Svetlana will have 4 * (2+x) = 8 + 4x coins...(2)

Svetlana has twice the number of coins that Junita has. So Junita has 1/2 of (8 + 4x) = 4 + 2x coins...(3)


Equating (1) and (3) 3x = 4 + 2x
x = 4


Number of coins Junita has before distribution = 6x = 24

Number of coins Svetlana has before the distribution = 8 + 4x - 2x = 8 + 2x = 16

The difference = 24 - 16 = 8


Option A

Arun Kumar
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Solution:

We can let 6x = the number of bitcoins Juanita currently has. So if she gives x bitcoins to Pat and 2x bitcoins to Svetlana (notice that x + 2x = 3x is half of 6x), then Pat will have 2 + x bitcoins and Svetlana will have 4(2 + x) = 8 + 4x bitcoins (notice that Pat having ¼ as many bitcoins as Svetlana means Svetlana having 4 times as many bitcoins as Pat). Since Svetlana will in turn have twice as many bitcoins as will Juanita, we can create the equation:

8 + 4x = 2(3x)

8 + 4x = 6x

8 = 2x

4 = x

Therefore, Juantia currently has 6x = 6(4) = 24 bitcoins.Svetlana will have 8 + 4(4) = 24 bitcoins if Juanita gives her 2(4) = 8 bitcoins. Therefore, Svetlana currently has 24 - 8 = 16 bitcoins and thus Juanita has 24 - 16 = 8 more bitcoins than Svetlana.

Answer: A

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Most information given is in ratio terms, so let's stick to ratio terms for now.
Juanita gives half in the ratio 1:2 so it means on ratio scale, Juanita will give 3 and will be left with 3 (Juanita has 6 right now).
After receiving 2 from Juanita, Svetlana will have 6 (twice as many as Juanita) so Svetlana has 4 right now.
Since Pat will have 1/4th as many as Svetlana, Pat will have 1.5 (after getting 1 from Juanita). So Pat has 0.5 currently.

In actual values, Pat has 2 so multiplier is 4 (because 0.5*4 = 2).
Since Juanita has 2 more than Svetlana in ratio terms, Juanita has 8 more than Svetlana actually.

Answer (A)
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