A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with same amount of cocoa powder to form a new mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16:9, then the ratio of cocoa in mixture P to that in mixture Q is
Question:
A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with same amount of cocoa powder to form a new mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16:9, then the ratio of cocoa in mixture P to that in mixture Q is
A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with same amount of cocoa powder to form a new mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16:9, then the ratio of cocoa in mixture P to that in mixture Q is
Options
Answer: 5:9
Explanation:
Let jar capacity be V and amount removed each time be x. After first operation, coffee fraction = (V-x)/V. After second operation, coffee fraction = (V-x)^2/V^2 = 16/25. So (V-x)/V = 4/5, meaning x/V=1/5. Cocoa in P = x = V/5. Cocoa in Q = V-16V/25 = 9V/25. Ratio = (V/5):(9V/25) = 5:9.
Explanation:
Let jar capacity be V and amount removed each time be x. After first operation, coffee fraction = (V-x)/V. After second operation, coffee fraction = (V-x)^2/V^2 = 16/25. So (V-x)/V = 4/5, meaning x/V=1/5. Cocoa in P = x = V/5. Cocoa in Q = V-16V/25 = 9V/25. Ratio = (V/5):(9V/25) = 5:9.
👉 Want AI explanation? Open in MCQ App
Recommended articles
- How To Cover Current Affairs For Upsc Prelims — Master UPSC Current Affairs with daily newspaper reading, Vision IAS monthly compilations, PT 365, and MCQ practice. Complete strategy guide for Prelims…
- Top 10 Daily Current Affairs Resources For Upsc Aspirants — Discover the best daily current affairs resources for UPSC 2026. Complete guide with The Hindu, PIB, Sansad TV, and 7 more proven sources. Expert…
- Free Cat Previous Year Questions Guide — Master CAT 2025 with free previous year questions. Practice 1000+ PYQs, mock tests, and detailed solutions. Complete guide to CAT preparation using past…