Question
Download Solution PDFHow much water should be added to 60 liters of milk at \(1 \frac{1}{2}\) liters a rupee so as to have a mixture worth \(1 \frac{7}{8}\) liters a rupee?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Initial amount of milk = 60 liters
Initial price of milk = \(1 \frac{1}{2}\) liters per rupee
Desired price of the mixture = \(1 \frac{7}{8}\) liters per rupee
Formula Used:
Value of milk = Volume of milk / Price
Value of mixture = Volume of mixture / Price
Calculation:
Let the amount of water added be x liters.
Initial value of milk = 60 / (3/2) = 60 × (2/3) = 40 rupees
Total volume of mixture = 60 + x liters
Desired value of mixture = (60 + x) / (15/8) = (60 + x) × (8/15) rupees
Setting the initial value equal to the desired value:
⇒ 40 = (60 + x) × (8/15)
⇒ 40 = (8/15) × (60 + x)
⇒ 40 × 15 = 8 × (60 + x)
⇒ 600 = 480 + 8x
⇒ 8x = 120
⇒ x = 120 / 8
⇒ x = 15 liters
The amount of water to be added is 15 liters.
Shortcut Trick As per question,
Initial:
Cost of 3/2 lt milk = 1 Rs
Cost of 1 lt milk = 1 * (2/3) = 2/3 Rs
Final:
Cost of 15/8 lt of mixture = 1 Rs
Cost of 1 lt of mixture = 8/15 Rs
Cost of water = 0 Rs
Now by using the allegation method, we get
⇒ Milk = 4 unit = 60 lt
⇒ 1 unit = 60/4 = 15 lt
⇒ Water = 1 unit = 15 lt
∴ The amount of water to be added is 15 liters.
Last updated on May 28, 2025
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