From a 100 ml can full of milk, 10 ml is removed and 20 ml water is ad

Question

From a 100 ml can full of milk, 10 ml is removed and 20 ml water is added. Next 20 ml of the solution is removed and 30 ml water is added. What is the quantity of milk in the solution now?

A. 800/11 ml
B. 810/11 ml
C. 820/11 ml
D. 830/11 ml
E. 840/11 ml

lacktutor · Answer

100 ml milk 
—> 100–10 =90 ml milk 
90ml(milk) + 20 ml(water) = 110ml solution 
 \frac{90}{110}= \frac{9}{11} 
—>  \frac{9}{11}  of 1 ml solution is milk

20ml solution is removed from 110ml solution: 
—> in the 20 solution, there is  (\frac{9}{11})*20 = \frac{180}{11} ml milk 
 90–\frac{180}{11} =\frac{( 990 —180)}{11} = \frac{810}{11} ml milk

In the 120ml solution, the quantity of milk is — \frac{810}{11}

The answer is B

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fauji · Answer

approach:

- quantity of milk and water after first step(10l milk out, 20ml water in): 90ml and 20ml, ratio 9:2
- now, 20 ml of solution (110 ml) is removed and filled with 30ml water.
- Milk left after removal:  90 -\frac{ 9}{11} *20=\frac{ (990-180)}{11} =\frac{ 810}{11}

Option B

Raome · Answer

Can someone explain why the following solution is wrong?

c1*v1/v2= c2
100 * (90/110) * (90/120) = 675/11

Bunuel · Answer

Your formula is wrong because it treats both operations as simple dilution. In this problem, milk is removed twice, so the fraction changes each time.

First operation:
Start with 100 ml milk. Remove 10 ml (all milk), leaving 90 ml milk. Add 20 ml water. Now total = 110 ml, so milk fraction = 90/110.

Second operation:
Remove 20 ml of this mixture. Milk removed = 20 * 90/110 = 180/11. Milk left = 90 - 180/11 = 810/11. Add 30 ml water. Total = 120 ml.

Final milk = 810/11 ml.

Bunuel · Answer

Your formula is wrong because it treats both operations as simple dilution. In this problem, milk is removed twice, so the fraction changes each time.

First operation:
 Start with 100 ml milk. Remove 10 ml (all milk), leaving 90 ml milk. Add 20 ml water. Now total = 110 ml, so milk fraction = 90/110.

Second operation:
 Remove 20 ml of this mixture. Milk removed = 20 × (90/110) = 180/11. Milk left = 90 − 180/11 = 810/11. Add 30 ml water. Total = 120 ml.

Final milk = 810/11 ml.

Fisayofalana · Answer

100ml of milk

subtract 10ml and add 20ml of water. Now the ratio is 90ml of milk: 20ml of water.
Milk represents ~82% of the total, and water represents ~ 18% of the total.

Next, subtract 20 ml. That 20 ml is made up of ~16ml of milk and ~4ml of water. So the new parts will be 74ml of milk to 16ml of water.

Add 30 ml of water. The new parts will be 74ml of milk to 46ml of water. Total = 120ml.

Find the answer closest to 74. 74 x 11 = 814. Closest is 810

From a 100 ml can full of milk, 10 ml is removed and 20 ml water is ad

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From a 100 ml can full of milk, 10 ml is removed and 20 ml water is ad

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