A milkman mixed 4 litres of water with 10 litres of
milk. He boiled one fourth of this mixture till the
water content in it, halved. Then he added it to
remaining mixture. What is the proportion of milk in
the mixture after the process?
(a) 7/10 (b) 18/15 (c) 21/27 (d) 20/27
Answer:
Correct Answer: Option B
Step-by-step explanation:
Given:
• A milkman mixed 4 liters of water with 10 liters of milk.
• He boiled one-fourth of this mixture till the water content in it halved.
o Then he added it to the remaining mixture.
To find:
• The proportion of milk in the mixture after the process.
Approach and Working out:
The volume of solution after mixing 4 liters of water with 10 liters of milk =14L
¾ of the solution that is kept as it is:
• Volume of solution that was not taken out = 14 – 3.5 = 10.5L.
o Milk and water in solution is in the ratio of 10:4 = 5:2
• Hence, quantity of milk in ¾ of the solution = × 10.5 =7.5L
o Quantity of water in ¾ of the solution = × 10.5 =3 L
¼ of this solution that is taken out.
• Volume of solution taken out = 14/4 = 3.5 L.
o Milk and water in 3.5L solution is in the ratio of 10:4 = 5:2
• Hence, quantity of milk in ¼ of the solution = × 3.5 =2.5L
o Quantity of water in ¼ of the solution = × 3.5 =1 L
This 3.5L of the mixture is boiled until the water quantity becomes half.
• New quantity of milk = Old quantity of milk = 2.5 L
• New quantity of water = ½ of 1 L = 0.5L
Now, this mixture is added to the original solution again.
• Total quantity of milk = 7.5 + 2.5 = 10L
• Total quantity of water = 3+0.5 = 3.5L
The proportion of milk after the process = =20/27
Hence, option B is the correct answer.