Question

Louis Pasteur mixes two acids HCL and HNO₃ in the ratio 7 ∶ 5 and filled it in a container. When 9 liters of solution is taken out and the can is filled with HNO₃, the ratio of HCL and HNO3 becomes 7 ∶ 9. How many liters of HCL was contained by the container initially?
1. 25 L
2. 21 L
3. 10 L
4. 20 L

Answer 1

Correct Answer - Option 2 : 21 L

Given∶

Initial ratio = 7 ∶ 5

9 liters of solution is taken out and the can is filled with HNO3 

New ratio = 7 ∶ 9

Formula Used∶

 

Basics of Ratios and Linear equations.

Calculation∶

Let the containers initially contains 7x and 5x of HCL and HNO3 respectively,

Quantity of HCL in solution left = [ 7x - 7/12 × 9 ] L = [ 7x - 21/4] L

Quantity of HNO3 in solution left = [ 5x - 5/12 × 9] L = [5x - 15/4] L

Resulting ratio,

⇒ [7x - 21/4] / [ 5x - 15/4] + 9 = 7/9

⇒ (28x - 21) / (20x + 21) = 7/9

⇒ 252 x - 189 = 140x + 147

⇒ 112x = 336

⇒ x = 336/112 = 3

Thus, Quantity of HCL = 7x = 7 × 3 = 21

∴ The containers contained 21 liters of HCL.