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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Correct Answer: 64 litres
Solution : Given: There are three cups of milk and water in ratios 4 : 5, 5 : 6, 9 : 7. In the first mixture of 36 litres, the quantity of milk = $36×\frac{4}{4+5}=36×\frac{4}{9}=16$ litres So, the quantity of water in the first mixture = 36 – 16 = 20 litres In the 2nd mixture of 44 litres, the quantity of milk = $44×\frac{5}{5+6}=44×\frac{5}{11}=20$ litres So, the quantity of water in the 2nd mixture = 44 – 20 = 24 litres Let the quantity of milk drawn from the third cup be $9x$ and the water quantity is $7x$. According to the question, $\frac{16+20+9x}{20+24+7x}=\frac{1}{1}$ $⇒36+9x=44+7x$ $\therefore x =4$ Quantity of mixture in the third cup = $9x+7x=16x=16×4=64$ litres Hence, the correct answer is 64 litres.
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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 : 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 : 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 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 : 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
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