Question : From a cask filled with wine, 75 litres are first drawn and replaced with water. From this mixture, 60 litres are drawn and replaced with water. The ratio of wine to water in the cask is now 3 : 2. How many litres of wine did the cask initially hold?
Option 1: 225
Option 2: 250
Option 3: 375
Option 4: 300
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 300
Solution : Let the cask initially hold $x$ litres of wine. After 75 litres are first drawn and replaced with water, Now, wine = ($x$ – 75) litres and water = 75 litres Ratio of wine and water = $(x–75) : 75$ Again, from this mixture, 60 litres are drawn and replaced with water. So, wine drawn = $60×(\frac{x–75}{x})$ litres and water drawn = $60×(\frac{75}{x})$ litres The wine's amount = $(x–75) – 60×(\frac{x–75}{x})$ litres According to the question, ($x–75) – 60×(\frac{x–75}{x})=\frac{3x}{5}$ $⇒2x^2–675x+22500=0$ $⇒(x–300)(2x–75)=0$ $⇒x=300$ (As $x$ can not be $\frac{75}{2}$) $\therefore$ the cask initially holds 300 litres of wine. Hence, the correct answer is 300.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : A cask having a capacity of 600 litres is initially filled with wine. From this cask $y$ litres of wine are first drawn and replaced with water. From this mixture, 120 litres are drawn and replaced with water. From this further diluted mixture. 120 litres are drawn again and
Question : In a mixture, the ratio of a chemical X and water is 15 : 9. When 48 litres of this mixture is replaced with water, the ratio becomes 11 : 13. Find the quantity of water after replacement.
Question : A mixture of 70 litres of wine and water contains 10% of water. How much water must be added to make the water $12 \frac{1}{2}\%$ of the resulting mixture?
Question : A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is:
Question : From a cask of milk containing 64 litres, 8 litres are drawn out and the cask is filled up with water. If the same process is repeated a second, then a third time, what will be the proportion of milk to water in the resulting mixture?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile