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Rahul removes a fraction of undiluted spirit and replaces it with wate 01 Jan 2020, 02:43
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D
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45% (medium)

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68% (02:07) correct 32% (02:26) wrong based on 310 sessions

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Rahul removes a fraction of undiluted spirit and replaces it with water to avoid detection. He does so on two continuous days. If spirit now accounts for only 64% of the solution, what fraction of solution did he remove daily?

A. 1/3
B. 2/3
C. 1/4
D. 1/5
E. 1/6
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D
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Rahul removes a fraction of undiluted spirit and replaces it with wate 01 Jan 2020, 18:48
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1*.8*.8=.64
Ans=D
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Rahul removes a fraction of undiluted spirit and replaces it with wate 02 Jan 2020, 12:23
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This kind of same percentage reduction can be done using multiplying factor equivalence
Let f be the factor by which it is reduced daily

So taking solution to be 100L

we have ,

100 *f*f =64
f=8/10
f =4/5

which indicated that 5 part is reduced to 4 part. Hence a difference of 1 part which indicates

1part /5 part = 20 % daily

hence fraction is 1/5. Answer is D
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Rahul removes a fraction of undiluted spirit and replaces it with wate 04 Jan 2020, 20:13
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Bunuel
Rahul removes a fraction of undiluted spirit and replaces it with water to avoid detection. He does so on two continuous days. If spirit now accounts for only 64% of the solution, what fraction of solution did he remove daily?

A. 1/3
B. 2/3
C. 1/4
D. 1/5
E. 1/6
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We can let the original amount of solution = 60 liters. Now let’s check the answer choices:

A. 1/3

On the first day, 1/3 x 60 = 20 liters of undiluted spirit were removed. Since 20 liters of water were added back in, we have 40 liters of the 60 liters are spirit.

On the second day, 1/3 x 40 = 40/3 liters of spirit (along with 1/3 x 20 = 20/3 liters of water) were removed, Since 20 liters of water were added back in, we have 40 - 40/3 = 80/3 liters of the 60 liters are spirit.
Since (80/3)/60 = 80/180 ≈ 44% ≠ 64%, A is not the correct answer.

We can skip B since the percentage would be even less than 44% had ⅔ of the solution been removed on each of the two days.

C. 1/4

On the first day, 1/4 x 60 = 15 liters of undiluted spirit were removed. Since 15 liters of water were added back in, we have 45 liters of the 60 liters are spirit.

On the second day, 1/4 x 45 = 45/4 liters of spirit (along with 1/4 x 15 = 15/4 liters of water) were removed, Since 15 liters of water were added back in, we have 45 - 45/4 = 135/4 liters of the 60 liters are spirit.

Since (135/4)/60 = 135/240 ≈ 56% ≠ 64%, C is not the correct answer.

D. 1/5

On the first day, 1/5 x 60 = 12 liters of undiluted spirit were removed. Since 12 liters of water were added back in, we have 48 liters of the 60 liters are spirit.

On the second day, 1/5 x 48 = 48/5 liters of spirit (along with 1/5 x 12 = 12/5 liters of water) were removed, Since 12 liters of water were added back in, we have 48 - 48/5 = 192/5 liters of the 60 liters are spirit.

Since (192/5)/60 = 192/300 = 64%, D is the correct answer.

Alternate Solution:

Let the amount of spirit be 100 liters and let the fraction of spirit Raul removes each day be k. Then, on the first day, there are 100*(1 - k) liters of spirit left and on the second day, there are 100*(1 - k)*(1 - k) = 100*(1 - k)^2 liters of spirit left. We are told that after the second day, the solution is 64% spirit, meaning that there are 100 * 0.64 = 64 liters of spirit in the solution. We can create the following equation:

100*(1 - k)^2 = 64

(1 - k)^2 = 64/100

1 - k = 8/10 = 4/5

k = 1 - 4/5 = 1/5

Answer: D
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Rahul removes a fraction of undiluted spirit and replaces it with wate 11 Apr 2025, 14:34
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