Question:
Two casks of 48 litres and 42 litres are filled with mixtures of milk and water, the proportions in the two casks being respectively, 13 : 7 and 18 : 17. If the contents of the two casks be mixed and 20 litres of water be added to the whole, what will be the proportion of milk and water in the resulting mixture?
Two casks of 48 litres and 42 litres are filled with mixtures of milk and water, the proportions in the two casks being respectively, 13 : 7 and 18 : 17. If the contents of the two casks be mixed and 20 litres of water be added to the whole, what will be the proportion of milk and water in the resulting mixture?
Updated On: Jan 30, 2025
- 5 : 12
- 7 : 13
- 12 : 13
- 8 : 15
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The Correct Option is C
Solution and Explanation
Quantity of milk in the mixture,
\(=\frac{13}{20}×48+\frac{18}{35}×42\)
\(=\frac{156}{6}+\frac{108}{5}=\frac{264}{5}L\)
Quantity of water in the mixture,
\(=\frac{7}{20}\times48+\frac{17}{35}\times42\)
\(=\frac{84}{5}+\frac{102}{5}=\frac{186}{5}L\)
20L of mixture is added to the mixture,
\(=\frac{186}{5}+20=\frac{186+100}{5}\)
\(=\frac{286}{5}L\)
Required ratio \(=\frac{264}{5}:\frac{286}{5}\)
\(=12:13\)
Hence, option C is the correct answer.The correct option is (C): 12 : 13
\(=\frac{13}{20}×48+\frac{18}{35}×42\)
\(=\frac{156}{6}+\frac{108}{5}=\frac{264}{5}L\)
Quantity of water in the mixture,
\(=\frac{7}{20}\times48+\frac{17}{35}\times42\)
\(=\frac{84}{5}+\frac{102}{5}=\frac{186}{5}L\)
20L of mixture is added to the mixture,
\(=\frac{186}{5}+20=\frac{186+100}{5}\)
\(=\frac{286}{5}L\)
Required ratio \(=\frac{264}{5}:\frac{286}{5}\)
\(=12:13\)
Hence, option C is the correct answer.The correct option is (C): 12 : 13
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