Question

A tank has a capacity of 10 gallons and is full of alchol. 2gallons of alchol drawnout and filled with water. process repeated 5 times. how much alchol left

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Concept:

If initial quantity of alcohol is a litres and b litres is drawn out n times and filled with b litres of the water, then the final volume of alcohol is given by,

Final volume = a×[(a-b)/a]ⁿ

Given:

Capacity of tank, a = 10 gallons

Volume of alcohol drawn out, b = 2 gallons

Volume of water filled in the tank, b = 2 gallons

Number of times process is repeated, n = 5 times

Find:

Volume of alcohol left in the tank.

Answer:

3.2768 gallons of alcohol is left in the tank.

Solution:

Let the volume of alcohol left in the tank be x.

Volume of alcohol left in the tank is given by,

x = a×[(a-b)/a]ⁿ

Putting the values in above formula, we get

x = 10 × [(10 - 2)/10]⁵

   = 10 × [8/10]⁵

   = 10 × [4/5]⁵

   = 10 × 4⁵/5⁵

   = 10 × 1024/3125

   = 2048/625

x = 3.2768 gallons

Hence, the volume of alcohol left in the tank is 3.2768 gallons.

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