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
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Correct Answer: 27 litres
Solution : Let the initial quantity of milk as $9x$ litres and the initial quantity of water as $5x$ litres. When 6 litres of water is added, the quantity of milk remains the same $9x $ litres, but the quantity of water increases to $(5x + 6)$ litres. The new ratio of milk to water is 9 : 7. $⇒\frac{9x}{5x + 6} = \frac{9}{7}$ $⇒63x = 45x + 54$ $⇒18x = 54$ $⇒x = 3$ So, the quantity of milk in the mixture is $9x = 9×3 = 27$ Hence, the correct answer is 27 litres.
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Question : 470 litres of a mixture of milk and water contains 5% of water. A mischievous boy added some water in the mixture and now there is 6% water in the new mixture. Find the quantity of water added by the boy in the mixture.
Option 1: 6 litres
Option 2: 8 litres
Option 3: 5 litres
Option 4: 10 litres
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 mixture of 180 litres, the ratio of milk and water is 5 : 1. If this ratio is to be 3 : 2, then find the quantity of water to be further added.
Option 1: 66 litres
Option 2: 70 litres
Option 3: 88 litres
Option 4: 72 litres
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 : There are three cups of milk and water in ratios 4 : 5, 5 : 6, 9 : 7. 36 litres of the first and 44 litres of the second cup are taken. How much quantity from the third cup is to be taken so that the final mixture from the three cups will have milk and water in a ratio 1 : 1?
Option 1: 32 litres
Option 2: 64 litres
Option 3: 54 litres
Option 4: 60 litres
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