Question : A mixture of milk and water in three bottles of equal capacity is in the ratio 4 : 1, 4 : 3, and 1 : 2, respectively. These three bottles are emptied into a large bottle. What will be the ratio of milk and water respectively in the large bottle?
Option 1: 179 : 136
Option 2: 152 : 165
Option 3: 198 : 175
Option 4: 133 : 145
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Correct Answer: 179 : 136
Solution : Let the capacity of each bottle be $x$. In the first bottle, quantity of milk $\frac{4}{5}x$ and quantity of water is $\frac{1}{5}x$. In the second bottle, quantity of milk $\frac{4}{7}x$ and quantity of water is $\frac{3}{7}x$. In the third bottle, quantity of milk $\frac{1}{3}x$ and quantity of water is $\frac{2}{3}x$. ⇒ Total quantity of milk = $\frac{4}{5}x$ + $\frac{4}{7}x$ + $\frac{1}{3}x$ = $\frac{84}{105}x$ + $\frac{60}{105}x$ + $\frac{35}{105}x$ = $\frac{179}{105}x$ ⇒ Total quantity of water = $\frac{1}{5}x$ + $\frac{3}{7}x$ + $\frac{2}{3}x$ = $\frac{21}{105}x$ + $\frac{45}{105}x$ + $\frac{70}{105}x$ = $\frac{136}{105}x$ So, the require ratio = $\frac{\text{Total quantity of milk}}{\text{Total quantity of water}}$ = $\frac{ \frac{179}{105}x}{ \frac{136}{105}x}$ = $\frac{179}{136}$ Hence, the correct answer is 179 : 136.
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Question : A bottle holds 8 litres of a mixture of milk and water in a ratio of 3 : 1. 3 litres of water is added to the given mixture. Find the new ratio of milk and water in the mixture.
Option 1: 3 : 2
Option 2: 1 : 3
Option 3: 2 : 3
Option 4: 6 : 5
Question : In a 255-litre mixture of milk and water, the ratio of milk and water is 4 : 1. Find the quantity of water required to make the ratio of milk and water 4 : 3.
Option 1: 94 litres
Option 2: 51 litres
Option 3: 102 litres
Option 4: 55 litres
Question : In a mixture, water and milk are in the ratio of 2 : 3. What is the amount of water that is to be added to 20 kg of this mixture to make the ratio of water and milk in the new mixture 1 : 1?
Option 1: 3 kg
Option 2: 2 kg
Option 3: 4 kg
Option 4: 5 kg
Question : A mixture contains milk and water in a ratio of 9 : 5. When 6 litres of water is added to this mixture, the ratio of milk and water becomes 9 : 7. Find the quantity of milk in the mixture.
Option 1: 30 litres
Option 2: 18 litres
Option 3: 27 litres
Option 4: 15 litres
Question : Two vessels of equal capacity, and both completely filled, contain mixtures of milk and water in the ratio of 5 : 1 and 6 : 5, respectively. Both the mixtures are now mixed thoroughly. What is the ratio of milk to water in the new mixture so obtained?
Option 1: 105 : 67
Option 2: 57 : 41
Option 3: 91 : 41
Option 4: 28 : 43
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