Question

Two containers, A and B, contain mixtures of alcohol and water. Container A has alcohol and water in the ratio 4:1, while Container B has them in the ratio 5:2. If 10 liters are drawn from Container A and 14 liters from Container B, and the contents are mixed in a third container, what is the ratio of alcohol to water in the new mixture?

• A. 3 : 1
• B. 7 : 2
• C. 9 : 4
• D. 11 : 3

Answer 1

Answer:

A. 3 : 1

Given:

• Container A: Alcohol : Water = 4 : 1

• Container B: Alcohol : Water = 5 : 2

• 10 L drawn from A

• 14 L drawn from B

Step 1: Find alcohol and water from Container A

Total parts = (4+1=5)

• Alcohol = $(\frac{4}{5}\times10=8) L$

• Water = $(\frac{1}{5}\times10=2) L$

Step 2: Find alcohol and water from Container B

Total parts = (5+2=7)

• Alcohol = $(\frac{5}{7}\times14=10) L$

• Water = $(\frac{2}{7}\times14=4) L$

Step 3: Add the quantities

• Total Alcohol = (8+10=18) L

• Total Water = (2+4=6) L

Therefore, the ratio of alcohol to water is

$18:6 = 3:1$

Answer:

$\boxed{3:1}$