the ratio of the quantities of hydrochloric acid to water in 48 litres of mixture is 5 : 3. how many litres of water should be added to the mixture to make their ratio 3 : 2.options (1)12 litres (2) 4 litres (3) 8 litres (4)2 litres
Answers
2 litres of water should be added to the mixture to make the ratio of hydrocholric acid and water equal to 3 : 2. Hence, option (4) is correct.
• Given,
Total volume of hydrocholric acid and water = 48 L
Ratio of HCl to H₂O in the mixture = 5 : 3 = 5x / 3x,
=> The quantity of HCl in the mixture = 5x
The quantity of H₂O in the mixture = 3x
• Now, the quantity of HCl and H₂O in the mixture sums up to the total quantity of the mixture.
=> 5x + 3x = 48 L
=> 8x = 48 L
=> x = 48 L / 8
=> x = 6 L
• The quantity of HCl in the mixture = 5x = 5 × 6 L = 30 L
The quantity of H₂O in the mixture = 3x = 3 × 6 L = 18 L.
• New ratio of HCl to H₂O in the mixture = 3 : 2
• Let the quantity of water added to the mixture be x.
New volume of water in the mixture = (18 L + x)
The quantity of HCl in the mixture remains same.
• Therefore, according to the question,
30 L : (18 L + x) = 3 : 2
=> 30 L / (18 L + x) = 3 / 2
On cross-multiplying,
30 L × 2 = 3 ( 18 L + x )
=> 60 L = 3 × 18 L + 3 × x
=> 60 L = 54 L + 3x
=> 3x = 60 L - 54 L
=> 3x = 6 L
=> x = 6 L / 3
=> x = 2 L
∴ 2 litres of water needs to be added to the mixture.
Answer:
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