Question:
A vessel contains an 80-liter mixture of milk and water containing 25% water. How many liters of water must be added so that the resulting mixture contains 40% water?
एक बर्तन में दूध और पानी का 80 लीटर मिश्रण है जिसमें 25% पानी है। इसमें कितना लीटर पानी मिलाया जाना चाहिए ताकि परिणामी मिश्रण में 40% पानी हो जाए?
Options:
- 20 liters
- 16 liters
- 18 liters
- 24 liters
- 20 लीटर
- 16 लीटर
- 18 लीटर
- 24 लीटर
Correct Answer: a)
Explanation:
Initial mixture = 80 liters.
Water = \(25\% \text{ of } 80 = 20\) liters.
Milk = \(80 – 20 = 60\) liters.
Let \(x\) liters of water be added. The quantity of milk remains unchanged at 60 liters.
In the new mixture, water is 40%, which means milk is \(100\% – 40\% = 60\%\).
So, \(60\% \text{ of (Total new mixture)} = 60\) liters.
Total new mixture = \(\frac{60}{0.60} = 100\) liters.
Water added \(x = 100 – 80 = 20\) liters.
Water = \(25\% \text{ of } 80 = 20\) liters.
Milk = \(80 – 20 = 60\) liters.
Let \(x\) liters of water be added. The quantity of milk remains unchanged at 60 liters.
In the new mixture, water is 40%, which means milk is \(100\% – 40\% = 60\%\).
So, \(60\% \text{ of (Total new mixture)} = 60\) liters.
Total new mixture = \(\frac{60}{0.60} = 100\) liters.
Water added \(x = 100 – 80 = 20\) liters.
प्रारंभिक मिश्रण = 80 लीटर
पानी = \(80 \times 25\% = 20\) लीटर, दूध = 60 लीटर
पानी मिलाने पर दूध की मात्रा 60 लीटर ही रहेगी।
नए मिश्रण में 40% पानी है, अतः दूध 60% होगा।
कुल नया मिश्रण = \(\frac{60}{60\%} = 100\) लीटर।
मिलाया गया पानी = \(100 – 80 = 20\) लीटर।
पानी = \(80 \times 25\% = 20\) लीटर, दूध = 60 लीटर
पानी मिलाने पर दूध की मात्रा 60 लीटर ही रहेगी।
नए मिश्रण में 40% पानी है, अतः दूध 60% होगा।
कुल नया मिश्रण = \(\frac{60}{60\%} = 100\) लीटर।
मिलाया गया पानी = \(100 – 80 = 20\) लीटर।