A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

Question

Accepted Answer

We are tasked with finding the ratio of water to acid in the original solution. Let the quantity of acid and water in the original solution be $$ A $$ litres and $$ W $$ litres, respectively.

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#### **Step 1: First condition (after adding 2 litres of water)**  
When 2 litres of water is added to the solution, the new solution has a 50% acid concentration. This means:  
$$
	ext{Amount of acid} = 	ext{Amount of water in the new solution}.
$$  
The total amount of water in the new solution is $$ W + 2 $$. Since the acid concentration is 50%, we have:  
$$
A = W + 2. 	ag{1}
$$

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#### **Step 2: Second condition (after adding 15 litres of acid)**  
When 15 litres of acid is added to the new solution, the final solution has an 80% acid concentration. The total volume of the final solution is:  
$$
A + 15 + W + 2 = A + W + 17.
$$  
Since the acid concentration is 80%, we have:  
$$
	ext{Amount of acid} = 80\% 	imes (	ext{Total volume}),
$$  
or:  
$$
A + 15 = 0.8(A + W + 17).
$$  
Simplify this equation:  
$$
A + 15 = 0.8A + 0.8W + 13.6,
$$  
$$
A - 0.8A = 0.8W + 13.6 - 15,
$$  
$$
0.2A = 0.8W - 1.4.
$$  
Divide through by $$ 0.2 $$:  
$$
A = 4W - 7. 	ag{2}
$$

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#### **Step 3: Solve for $$ A $$ and $$ W $$**  
From Equation (1):  
$$
A = W + 2.
$$

From Equation (2):  
$$
A = 4W - 7.
$$

Equate the two expressions for $$ A $$:  
$$
W + 2 = 4W - 7,
$$  
$$
3W = 9,
$$  
$$
W = 3.
$$

Substitute $$ W = 3 $$ into Equation (1):  
$$
A = W + 2 = 3 + 2 = 5.
$$

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#### **Step 4: Find the ratio**  
The original quantities of water and acid are $$ W = 3 $$ and $$ A = 5 $$, respectively. The ratio of water to acid is:  
$$
W : A = 3 : 5.
$$

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### **Final Answer:** The ratio of water to acid in the original solution is **3 : 5**.

Answer

Answer

Answer