Question

A cistern contains 100 liters of pure syrup. 10 liters of syrup are drawn out and replaced by water. Then, 10 liters of the mixture are drawn out and replaced by water again. What is the ratio of syrup to water in the final mixture?

• A. 18 : 1
• B. 89 : 14
• C. 81 : 19
• D. 18 : 17

Answer 1

Answer:

C. 81 : 19

This is a replacement (alligation) problem.

Initial amount:

• Syrup = 100 L

• Water = 0 L

After the 1st replacement:

• 10 L syrup removed.

• Syrup left = 90 L

• Water added = 10 L

So the mixture is:

• Syrup = 90 L

• Water = 10 L

After the 2nd replacement:
10 L of the mixture is removed.

Fraction of syrup in the mixture = (90/100)

So syrup removed:
$10 \times \frac{90}{100} = 9 \text{ L}$

Water removed:
$10 \times \frac{10}{100} = 1 \text{ L}$

Remaining:

• Syrup = (90 - 9 = 81) L

• Water = (10 - 1 = 9) L

Now add 10 L water:

• Syrup = 81 L

• Water = (9 + 10 = 19) L

Therefore, the final ratio of syrup : water is

$\boxed{81:19}$

Answer: 81 : 19