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A container originally contains $10$ litres of pure spirit. From this container, $1$ litre of spirit replaced with $1$ litre of water. Subsequently, $1$ litre of the mixture is again replaced with $1$ litre of water and this process is repeated one more time. How much spirit is now left in the container?

  1. $7.58$ litres
  2. $7.84$ litres
  3. $7$ litres
  4. $7.29$ litres
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4 Answers

Best answer
34 votes
34 votes
Quantity left after $n$ operations $=x\left(1 -\dfrac{y}{x}\right)^{n}$
where, $x=$ initial quantity    
             $y=$ amount of mixture withdrawn each time (this should be same every time)
             $n=$ no. of times operation performed

$\quad = 10\left(1 -\dfrac{1}{10}\right)^{n}$
$\quad =10 \left(\dfrac{9}{10}\right)^{3}$
$\quad = 10\times 0.9\times 0.9\times 0.9$
$\quad = 10\times 0.729 = 7.29$ litres

Hence, option $D$ is correct.
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15 votes
15 votes
Initial = 10L of spirit

stage 1:-

Take out 1 L of  S and add 1 L of W

9L of S + 1L of W

stage 2:-

1 L of this mixture contains 0.9 L of S and 0.1 L of W

Take out 1 L of above mixture and add 1 L of W

satge 3:-

Currently 10 L = 8.1 L of S + 1.9 L of W

1 L of this mixture contains 0.81 L of S and 0.19 L of W

Take out 1 L of above mixture and add 1 L of W

stage 4:

Currently 10 L = 7.29 L of S + 2.71 L of W

 

Hence the mixture contains 7.29 L of Spirit and 2.71 L of Water at final stage ie Ans is ==> D)
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2 votes
2 votes
Don't think about adding water. As how much of spirit is taken out that much water will be added.

First time you take out 1 litre of spirit or 1/10th of original capacity which is (10 litres*1/10) is taken out.. So 9 Litres remain. Rest is water.

Next time again 1/10th of the mixture which contains both spirit and water is taken out.
Lets consider only spirit. Total spirit was 9 Litres. 9 Litres * 1/10 = 8.1 litres spirit remains. Here 1/10 and not 1/9 because we are considering total mixture which is 10 litres only..

Again if we take 8.1 litres * 1/10th = 7.29 Litres of Spirit..
1 votes
1 votes
Percentage of spririt take out = $1/10*100 = 10  \% $

now 1 st time → $10 litre$ – $1*10/100$ = $9 litre  $ sprit Remains

2nd time  → $9- 9*10/100=8.1 litre $

3rd Time → $8.1-8.1*10/100= 7.29 litre$.
Answer:

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