Question

There are 1000 litres of milk in a pot.100 litres of milk is taken out and the same amount of water is poured into it. Again 200 litres of mixture is taken out and the same amount of water is poured into it and finally 400 litres of mixture is taken out and the same amount of water is poured into it then what is the amount of milk in the resulting mixture.
A.432
B.436
C.425
D.438

Answer 1

Hint: Initially there are 1000 litres of milk and when 100 l milk is removed and 100 litre water is added the ratio of milk is to water becomes 9:1 and from that solution 200 litres is removed and 200 litres of water is added . First we need to calculate the amount of milk and water in the solution removed using the ratio and subtract it from the total amount of milk and water in the previous step. We need to repeat this again for the next process and with the final ratio we can calculate the amount of milk and water.

Complete step-by-step answer:
Step 1: There are three process in the above problem
Process 1:Removing 100 l milk and adding 100 l water
Process 2: Removing 200 l solution ( milk and water) and adding 200 l water
Process 3: Removing 400 l solution (milk and water) and adding 400 l water
Step 2: Before any process there is 1000 l of milk in the pot
By process 1 we removed 100 l of milk and added 100 l of water
Therefore the solution contains 900 l milk and 100 l water
From this the ratio of milk to water is given by
$
   \Rightarrow 900:100 \\
   \Rightarrow 9:1 \\
$
(we need to remember that there are totally 10 parts)
Step 3:
In the second process 200 l of solution is removed and 200 l of water is added.
Therefore , out of 200 l of solution that is to be removed 9 parts will be milk and 1 part will be water.
Milk removed =$200*\dfrac{9}{{10}} = 180l$
Water removed =$200*\dfrac{1}{{10}} = 20l$
After process 1 we had 900 l of milk and 100 l of water.
And now , amount of milk = 900 – 180 =720 l
                   amount of water=100 – 20 +200 =280 l(the 200 l of water was added in process 2)
So now the ratio of milk to water is given by
 $
   \Rightarrow 720:280 \\
   \Rightarrow 36:14 \\
   \Rightarrow 18:7 \\
$
(here we have totally 25 parts)
Step 4
In the third process 400 l of solution is removed and 400 l of water is added.
Therefore , out of 400 l of solution that is to be removed 18 parts will be milk and 7 parts will be water.
Milk removed =$400*\dfrac{{18}}{{25}} = 288l$
Water removed =$400*\dfrac{7}{{25}} = 112l$
After process 2 we had 720 l of milk and 280 l of water.
And now , amount of milk = 720 – 288 =432 l
 Amount of water=280 – 112 +400 =568 l(the 400 l of water was added in process 3)
There the amount of milk at the end is 432 l
The correct option is A.

Note: 1.A ratio between two or more quantities is a way of measuring their sizes compared to each other
2.While finding ratio we need to make sure both the quantities are of the same units. If one quantity is in litre and another is in millilitre then we have to convert both to either litre or millilitre.