QuestionA 100L tank has 10L of milk removed twice, then filled with water. What % of milk remains? (a) 80% (b) 81% (c) 85% (d) None

Studdy Solution

STEP 1

Assumptions1. The tank initially contains100 litres of milk. .10 litres of milk are removed twice and replaced with water each time.
3. We need to find the percentage of milk left in the tank after these operations.

STEP 2

First, we need to calculate the quantity of milk left after the first operation. This can be done by subtracting the quantity of milk taken out from the initial quantity.
$Milk_{after\,first\,operation} = Initial\,quantity - Quantity\,taken\,out$

STEP 3

Now, plug in the given values for the initial quantity and the quantity taken out to calculate the quantity of milk left after the first operation.
$Milk_{after\,first\,operation} =100\,litres -10\,litres$

STEP 4

Calculate the quantity of milk left after the first operation.
$Milk_{after\,first\,operation} =100\,litres -10\,litres =90\,litres$

STEP 5

After the first operation, the tank is filled back up with water, so the total volume in the tank remains100 litres. Now, we need to calculate the percentage of the tank that is milk after the first operation.
$Percentage\,of\,milk_{after\,first\,operation} = \frac{Milk_{after\,first\,operation}}{Total\,volume} \times100\%$

STEP 6

Plug in the values for the quantity of milk left after the first operation and the total volume to calculate the percentage of milk after the first operation.
$Percentage\,of\,milk_{after\,first\,operation} = \frac{90\,litres}{100\,litres} \times100\%$

STEP 7

Calculate the percentage of milk after the first operation.
$Percentage\,of\,milk_{after\,first\,operation} = \frac{90\,litres}{100\,litres} \times100\% =90\%$

STEP 8

The same operation is repeated a second time. The quantity of milk left after the second operation is the percentage of milk after the first operation times the quantity of milk left after the first operation.
$Milk_{after\,second\,operation} = Percentage\,of\,milk_{after\,first\,operation} \times Milk_{after\,first\,operation}$

STEP 9

Plug in the values for the percentage of milk after the first operation and the quantity of milk left after the first operation to calculate the quantity of milk left after the second operation.
$Milk_{after\,second\,operation} =90\% \times90\,litres$

STEP 10

Convert the percentage to a decimal value.
$90\% =0.9$ $Milk_{after\,second\,operation} =0.9 \times90\,litres$

STEP 11

Calculate the quantity of milk left after the second operation.
$Milk_{after\,second\,operation} =0.9 \times90\,litres =81\,litres$

STEP 12

Finally, we need to calculate the percentage of the tank that is milk after the second operation.
$Percentage\,of\,milk_{after\,second\,operation} = \frac{Milk_{after\,second\,operation}}{Total\,volume} \times100\%$

STEP 13

Plug in the values for the quantity of milk left after the second operation and the total volume to calculate the percentage of milk after the second operation.
$Percentage\,of\,milk_{after\,second\,operation} = \frac{81\,litres}{100\,litres} \times100\%$

STEP 14

Calculate the percentage of milk after the second operation.
$Percentage\,of\,milk_{after\,second\,operation} = \frac{81\,litres}{100\,litres} \times100\% =81\%$ The quantity of milk left in the tank is81%.

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