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+19 votes

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?

- $7.58$ litres
- $7.84$ litres
- $7$ litres
- $7.29$ litres

+28 votes

Best answer

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$y=$ amount of mixture withdrawn each time (this should be same every time)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.

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$y=$ amount of mixture withdrawn each time (this should be same every time)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.

+5

$10 l$ initially

After $1^{st}$ replacement: $9l$ spirit + $1l$ water $(mixture)$

$1l$ mixture is again replaced. Means $\dfrac{9}{10}\times 1l=0.9l\ spirit\ removed$

After $2^{nd}$ replacement: $9-0.9=8.1$ spirit + $1.9l$ water

$1l$ mixture is again replaced. Means $\dfrac{8.1}{10}\times 1l=0.81l\ spirit\ removed$

After $3^{rd}$ replacement: $8.1-0.81=7.29$ spirit + $2.71l$ water

$\therefore\ 7.29l\ spirit\ is\ left$

After $1^{st}$ replacement: $9l$ spirit + $1l$ water $(mixture)$

$1l$ mixture is again replaced. Means $\dfrac{9}{10}\times 1l=0.9l\ spirit\ removed$

After $2^{nd}$ replacement: $9-0.9=8.1$ spirit + $1.9l$ water

$1l$ mixture is again replaced. Means $\dfrac{8.1}{10}\times 1l=0.81l\ spirit\ removed$

After $3^{rd}$ replacement: $8.1-0.81=7.29$ spirit + $2.71l$ water

$\therefore\ 7.29l\ spirit\ is\ left$

+10 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)

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)

0

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

Can you explain next step??

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

Can you explain next step??

+4

In case anyone needs elaboration of stage2

After taking out 1L of spirit and pouring 1L of water in stage 1, the ratio of spirit:water becomes 9:1.

So in 10L of mixture, 9L of Spirit and 1L of Water.

Similarly,** in 1L of mixture, 9/10L=0.9L of Spirit and 0.1L of water will be there.**

Now at this stage we are taking out 1L of mixture (containing 0.9L of spirit and 0.1L of water) and in the bucket there is 9L left of which 9*0.9L=8.1L is spirit and 9*0.1L=0.9L of water is there.

Adding 1L of water to this.

**Spirit volume remains 8.1L and water becomes 0.9L+1L=1.9L**.

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