A vessel is full of mixture of spirit and water in which there is 20

method 1

let total vol of mixture be x
so
20/100 * x be spirit and drawn off spirit ; 20/100 * 5 ; 1
we get
20/100 * x - 1 = 12/100 * x
20x-100 = 12x
8x =100
x= 12.5
OPTION B

OR method 2
∆ in % of spirit = 20-12 ; 8%
so drawn of mix has 5/8 of spirit
so 20% would have total mix
20*5/8 = 12.5 liters
OPTION B

A vessel is full of mixture of spirit and water in which there is 20 per cent of spirit. 5 litres are drawn off and the vessel is filled up with water. If the spirit is now 12 %, find the total capacity of the vessel (in Itrs).

A. 7.2
B. 12.5
C. 16
D. 20
E. None of these

For the purpose of approximation,
We can take one value like 12.5 from the options and apply the process.
12.5 will be split into water= 80%= 10 and spirit= 20%= 2.5
If we take out 5 litres from the solution, it means we take out 4 ltrs of water and 1 litre of spirit. Then we fill 5 litres of water.
So finally we get 11 lts of water and 1.5 lts of spirit.
Ratio of spirit in the final solution= 1.5/ 12.5= 12 percent.
Answer: B

Given:
1. A vessel is full of mixture of spirit and water in which there is 20 per cent of spirit.
2. 5 litres are drawn off and the vessel is filled up with water.

Asked: If the spirit is now 12 %, find the total capacity of the vessel (in Itrs).

Let the total capacity of the vessel be x litres
1. A vessel is full of mixture of spirit and water in which there is 20 per cent of spirit.
Spirit = .2x; Water = .8x

2. 5 litres are drawn off and the vessel is filled up with water.
Spirit = .2(x-5) = .2x -1; Water = x - .2(x-5) = .8x +1

The spirit is now 12 %
(.2x -1)/x = .12; .2x-1=.12x; .08x = 1; x = 1/.08 = 12.5 litres

IMO B

A vessel is full of mixture of spirit and water in which there is 20 per cent of spirit. 5 litres are drawn off and the vessel is filled up with water. If the spirit is now 12 %, find the total capacity of the vessel (in Itrs).

Assume the original volume of the vessel is Z. Z consists of both spirit and water.
Spirit volume = 0.2Z
Water volume = 0.8Z

Now, 5 litres are drawn out from the vessel. Since the ratio of spirit and water is known, the volume out is:
Spirit volume out: 0.2 x -5L = -1L
Water volume out: -5L + 1L = -4L

After the exercise, fresh 5L water is added to the tank and the spirit concentration becomes 12%.
Spirit volume final: 0.2Z - 1L
Water volume final: 0.8Z - 4L + 5L = 0.8Z + 1L

The final spirit concentration can be obtained by dividing the final volume of Spirit over the overall volume
(0.2Z - 1L) / (0.2Z - 1L + 0.8Z + 1L) = 12%
(0.2Z - 1L) / Z = 12%
0.2Z - 0.12Z = 1L
Hence, Z = 12.5L (B)

Let:
- Total volume = \(V\)
- Prior concentration of spirit = \(\frac{1}{5}\)

Current concentration of spirit after a replacement:
\(\frac{1}{5}*(1-\frac{5}{V}) = \frac{12}{100}\)
\((1-\frac{5}{V}) = \frac{60}{100}\)
\(\frac{5}{V}= \frac{40}{100}\\
= \frac{2}{5}\)
\(V=5*\frac{5}{2}=12.5\) litres

FINAL ANSWER IS (B)

Posted from my mobile device

A vessel is full of mixture of spirit and water in which there is 20 per cent of spirit. 5 litres are drawn off and the vessel is filled up with water. If the spirit is now 12 %, find the total capacity of the vessel (in Itrs).

A. 7.2
B. 12.5
C. 16
D. 20
E. None of these

Let V be the capacity of the vessel.

V/5 = spirit
4V/5 = Water

5 litres are drawn => 1 litre of spirit and 4 litres of water is drawn and 5 litres of water are added => 1 litre of water is added for 1 litre of spirit drawn

V/5 - 1 = Spirit
4V/5 + 1 = Water

(V/5 - 1)/V = 12/100
100(V-5) = 60V
40V = 500
V = 12.5

Answer - B

Suppose P litres total capacity.
Initial proportion given => W= 0.8P, S=0.2P
When drawing 5 litres of solution , proportion will be W=0.8P-(0.8*5), S=0.2P-(0.2*5)
When we add 5 litres of water only water proportion will be affected , W= 0.8P-4+(1*5) (As 100% water is added 5 will be multiplied by 1)
Now, we have been told the proportion of spirit now becomes 12%
So, (Spirit/total)*100 = {0.2P-1/(0.2P-1+0.8P+1)}*100 which Yields P=12.5 Litres

Hence Ans . B

let x=capacity
.8(x-5)+5=.88x→
x=12.5 liters
B

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.