There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is
Question:
There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is
There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is
Options
Answer: (1) 5:6
Explanation:
Let the capacity of each container be V. Initial: Container 1: V/2 syrup, 0 milk Container 2: 0 syrup, V/2 milk Step 1: Transfer half of container 1 (V/4) to container 2. Container 1: V/4 syrup Container 2: V/4 syrup + V/2 milk = 3V/4 total • Syrup fraction in container 2 = 1/3 • Milk fraction in container 2 = 2/3 Step 2: Transfer half of container 2 (3V/8) to container 1. Amount transferred: • Syrup transferred = (1/3)(3V/8) = V/8 • Milk transferred = (2/3)(3V/8) = V/4 After transfer: Container 1: • Syrup = V/4 + V/8 = 3V/8 • Milk = V/4 • Total = 5V/8 Container 2: • Syrup = V/4 − V/8 = V/8 • Milk = V/2 − V/4 = V/4 • Total = 3V/8 Step 3: Transfer half of container 1 (5V/16) to container 2. Composition of container 1 before transfer: • Syrup fraction = (3V/8) / (5V/8) = 3/5 • Milk fraction = 2/5 So in the transferred 5V/16: • Syrup = (3/5)(5V/16) = 3V/16 • Milk = (2/5)(5V/16) = V/8 Add to container 2: Final contents in container 2: • Syrup = V/8 + 3V/16 = 5V/16 • Milk = V/4 + V/8 = 6V/16 Final ratio in container 2 = syrup : milk = 5 : 6 Correct answer: 5:6
Explanation:
Let the capacity of each container be V. Initial: Container 1: V/2 syrup, 0 milk Container 2: 0 syrup, V/2 milk Step 1: Transfer half of container 1 (V/4) to container 2. Container 1: V/4 syrup Container 2: V/4 syrup + V/2 milk = 3V/4 total • Syrup fraction in container 2 = 1/3 • Milk fraction in container 2 = 2/3 Step 2: Transfer half of container 2 (3V/8) to container 1. Amount transferred: • Syrup transferred = (1/3)(3V/8) = V/8 • Milk transferred = (2/3)(3V/8) = V/4 After transfer: Container 1: • Syrup = V/4 + V/8 = 3V/8 • Milk = V/4 • Total = 5V/8 Container 2: • Syrup = V/4 − V/8 = V/8 • Milk = V/2 − V/4 = V/4 • Total = 3V/8 Step 3: Transfer half of container 1 (5V/16) to container 2. Composition of container 1 before transfer: • Syrup fraction = (3V/8) / (5V/8) = 3/5 • Milk fraction = 2/5 So in the transferred 5V/16: • Syrup = (3/5)(5V/16) = 3V/16 • Milk = (2/5)(5V/16) = V/8 Add to container 2: Final contents in container 2: • Syrup = V/8 + 3V/16 = 5V/16 • Milk = V/4 + V/8 = 6V/16 Final ratio in container 2 = syrup : milk = 5 : 6 Correct answer: 5:6
👉 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…