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470 liters 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.
6 litres
8 litres
5 litres
10 litres
- We begin with an initial mixture containing 470 liters, composed of 5% water.
- This results in the initial water content as 5% of 470 liters: 0.05×470=23.5 liters.
- After the mischievous act, the water percentage increases to 6%.
- Let the amount of water added be x liters.
- The new total water content becomes 23.5+x liters.
- The new mixture total remains 470 + x liters.
- The equation for the new water percentage is 23.5+x470+x=0.06.
- Solving this, 23.5+x=0.06×(470+x).
- Simplifying gives 23.5+x=28.2+0.06x.
- Solving for x leads to x=5 liters.
So, Option 3: 5 liters is the correct choice.
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