Question

A can contains a mixture of two liquids, A and B in the ratio 7 : 5. When 9 litres of mixture is drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially ?

• A. 14
• B. 21
• C. 35
• D. 28
• E. 20

Hint:

In mixture problems, track the quantity of each component separately. Use fractions to avoid decimals.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Mixture replacement logic. The ratio of the component not being added remains constant in its relative parts.
Step 2: Key Formula or Approach:
Let initial parts be 7x and 5x. After removing 9L, the ratio remains 7:5.
Step 3: Detailed Explanation:
Initial Total = 12x.
1. After removing 9L, Liquid A remaining = \( 7x - \frac{7}{12}(9) \).
2. After removing 9L and adding 9L of B, Liquid B = \( 5x - \frac{5}{12}(9) + 9 \).
3. New ratio: \( \frac{7x - 5.25}{5x + 3.75} = \frac{7}{9} \).
Simplifying: \( 9(7x - 5.25) = 7(5x + 3.75) \implies 63x - 47.25 = 35x + 26.25 \).
\( 28x = 73.5 \) ??? Let's use parts logic.
Ratio change: A remains 7 units. B changes from 5 to 9 (+4 units).
These 4 units of B must equal the 9L added.
1 unit = 2.25L.
Total volume after drawing mixture = 12 units \(\times\) 2.25 = 27L.
Initial total volume = 27 + 9 (removed) = 36L.
Initial A = \( \frac{7}{12} \times 36 = 21 \) L.
Step 4: Final Answer:
Initial volume of A was 21 litres.