Rahul removes a fraction of undiluted spirit and replaces it with wate

Question

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

A. 1/3
B. 2/3
C. 1/4
D. 1/5
E. 1/6

brains · Accepted Answer

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

tbhauer · Answer

1*.8*.8=.64
Ans=D

ScottTargetTestPrep · Answer

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

versewriter7 · Answer

We can solve this question through putting values given in the options.

Lets choose option (c) i.e. 1/4

So Let we assume 100 liter was the undiluted spirit and in day no 1, 1/4 was removed and replaced with water, so resultant will be 75 is in Spirit and 25 will be water.

After on Second day, 1/4 was removed and added the water. So the the resultant will be 56.25 in Spirit and 43.75 in water, The said result does not matches with the 64% as mentioned in the question. So option c is not right

But if we choose option D the said result i.e. 64% is matches with the result.

So initially there is 100 liter of spirit. 1/5 was replace two time i.e. on first day and second day. So on first day solution will be after replacement 80 and 20. On second day the solution will be 64 and 36, which matches with the 64% of Spirit. So option D is our answer

Rahul removes a fraction of undiluted spirit and replaces it with wate

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Rahul removes a fraction of undiluted spirit and replaces it with wate

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