A Container contains 192 liter of Milk. A seller draws out x% of Milk ...
Answer – 5. 25% Explanation : 81 = 192(1-x/100)³ x = 25
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A Container contains 192 liter of Milk. A seller draws out x% of Milk ...
As we Know,
Amount of milk left=((1-(Amount drawn/Initial quantity))^(no of times performed)) *initial quantity
but here amount drawn is given in %
So,81=((1-x/100)^3) *192
81/192= 27/64=(1-x/100)^3
or 1-x/100=3/4
or x=25%
A Container contains 192 liter of Milk. A seller draws out x% of Milk ...
Given:
- Initial quantity of milk in the container = 192 liters
- The seller repeats the process of withdrawing x% of milk and replacing it with the same quantity of water for 3 times.
- The quantity of milk in the mixture after 3 replacements = 81 liters
To find:
- The percentage of milk withdrawn by the seller at each step.
Solution:
Let's assume that the percentage of milk withdrawn by the seller at each step is 'p'.
Step 1:
- In the first step, the seller withdraws p% of milk from the container.
- The remaining milk in the container = (100 - p)% of 192 liters = (100 - p)/100 * 192 liters
- The seller replaces the withdrawn milk with an equal quantity of water.
- So, the quantity of milk in the container after the first replacement = (100 - p)/100 * 192 liters - (p/100 * 192 liters) + (p/100 * 192 liters) = (100 - p)/100 * 192 liters
Step 2:
- In the second step, the seller again withdraws p% of milk from the container.
- The remaining milk in the container after the second step = (100 - p)% of [(100 - p)/100 * 192 liters] = (100 - p)/100 * (100 - p)/100 * 192 liters
- The seller replaces the withdrawn milk with an equal quantity of water.
- So, the quantity of milk in the container after the second replacement = (100 - p)/100 * (100 - p)/100 * 192 liters - (p/100 * (100 - p)/100 * 192 liters) + (p/100 * (100 - p)/100 * 192 liters) = (100 - p)/100 * (100 - p)/100 * 192 liters
Step 3:
- In the third step, the seller once again withdraws p% of milk from the container.
- The remaining milk in the container after the third step = (100 - p)% of [(100 - p)/100 * (100 - p)/100 * 192 liters] = (100 - p)/100 * (100 - p)/100 * (100 - p)/100 * 192 liters
- The seller replaces the withdrawn milk with an equal quantity of water.
- So, the quantity of milk in the container after the third replacement = (100 - p)/100 * (100 - p)/100 * (100 - p)/100 * 192 liters - (p/100 * (100 - p)/100 * (100 - p)/100 * 192 liters) + (p/100 * (100 - p)/100 * (100 - p)/100 * 192 liters) = (100 - p)/100 * (100 - p)/100 * (100 - p)/100 * 192 liters
Final equation:
- The quantity of milk in the container after 3 replacements = (100 - p)/100 * (100 - p)/100 * (100 - p)/100 * 192 liters = 81 liters
Solving the equation:
- (100 - p)/100 * (100 - p)/100 * (100 - p)/