From a 54 litre vessel filled with acid, X litres was poured out and water was added instead, then the same quantity of the mixture was poured out again. After this the mixture in the vessel contained 24 litres of pure acid. How much acid was first poured out? radio_button_unchecked 22 litre radio_button_unchecked 20 litre radio_button_unchecked 18 litre radio_button_unchecked 16 litre
Question
From a 54 litre vessel filled with acid, X litres was poured out and water was added instead, then the same quantity of the mixture was poured out again. After this the mixture in the vessel contained 24 litres of pure acid. How much acid was first poured out?
radio_button_unchecked 22 litre
radio_button_unchecked 20 litre
radio_button_unchecked 18 litre
radio_button_unchecked 16 litre
Solution
Let's denote the quantity of acid that was first poured out as X litres.
Step 1: Initially, the vessel was filled with 54 litres of acid. After X litres of acid was poured out, the vessel contained (54 - X) litres of acid.
Step 2: Then, X litres of water was added to the vessel. So, the vessel still contained (54 - X) litres of acid, but now it also contained X litres of water.
Step 3: Then, X litres of the mixture was poured out. Since the mixture was a uniform mixture of acid and water, the proportion of acid in the X litres that was poured out was the same as the proportion of acid in the vessel. So, the quantity of acid that was poured out was X * [(54 - X) / 54] litres.
Step 4: After X litres of the mixture was poured out, the vessel contained (54 - X) - X * [(54 - X) / 54] litres of acid.
Step 5: According to the problem, after all these operations, the vessel contained 24 litres of acid. So, we have the equation (54 - X) - X * [(54 - X) / 54] = 24.
Step 6: Solving this equation for X, we find that X = 20 litres.
So, the quantity of acid that was first poured out was 20 litres. Therefore, the correct answer is:
radio_button_checked 20 litre
Similar Questions
How many litres of water should be added to 24 litres of an acid and water solution, such that the concentration of acid in the solution decreases from 60% to 45%?
Select the correct answerThere are two water tanks A and B. A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160….., in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, and so on). If tank B is 1/16 filled after 17 hours, what is the total duration required to fill it completely?radio_button_unchecked4 hoursradio_button_unchecked21 hoursradio_button_unchecked22 hoursradio_button_unchecked24 hours
48 litre of Glycerin is mixed with 144 litre Rose water. D litre of total mixture is taken out and 32 litre Glycerin and 48 litre Rose water are added in the mixture. The final mixture contains 30% Glycerin, find the quantity of the mixture that is taken out.Choices:- 24 32 40 20
Give the answer as a mixed number in its simplest form.A tank had 78 ℓ of water. 34 of the water was used to put out a fire.How many litres of water were used?
A milkman had 20 litres of pure milk. He removed some milk and added an equal amount of water. He repeated the process again. Now, the milk was only 64% pure. Find the amount of milk that he removed initially.Choices:- 4 litres 6 litres 6.6 litres 5 litres
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.