A mixture of acid and water has a volume of 164 liters with ratio of a

1.	A mixture of acid and water has a volume of 164 liters with ratio of acid to water as 21 : 20. What volume of the mixture have to be replaced with 10 liters of water so that the ratio becomes 1 : 4?1. 157.6 liters2. 124.7 liters3. 152.7 liters4. 162 liters5. None of these
Answer» Correct Answer - Option 1 : 157.6 liters Given: Initial quantity of mixture = 164 liters Acid : Water = 21 : 20 Concept: When replacing the mixture with water, quantity of acid will only decrease whereas quantity of water will first decrease and then increase. Calculations: Initial quantity of acid = 164 × 21/41 = 84 liters Initial quantity of water = 164 – 84 = 80 liters Let us assume the volume of mixture that has to be replaced by 10 liters of water = 41x [Note how we are choosing the values so that we can avoid complicated fractions] In 41x liters mixture, Quantity of acid = 21x liters Quantity of water = 20x liters ∴ Final quantity of acid = (84 – 21x) liters ∴ Final quantity of water = (80 – 20x + 10) liters = (90 - 20x) liters ATQ, (84 – 21x)/ (90 - 20x) = ¼ ⇒ 336 – 84x = 90 – 20x ⇒ x = 246/64 = 123/32 ∴ Quantity of mixture to be replaced = 123/32 × 41 = 157.6 liters

A mixture of acid and water has a volume of 164 liters with ratio of acid to water as 21 : 20. What volume of the mixture have to be replaced with 10 liters of water so that the ratio becomes 1 : 4?1. 157.6 liters2. 124.7 liters3. 152.7 liters4. 162 liters5. None of these

Answer» Correct Answer - Option 1 : 157.6 liters

Given:

Initial quantity of mixture = 164 liters

Acid : Water = 21 : 20

Concept:

When replacing the mixture with water, quantity of acid will only decrease whereas quantity of water will first decrease and then increase.

Calculations:

Initial quantity of acid = 164 × 21/41 = 84 liters

Initial quantity of water = 164 – 84 = 80 liters

Let us assume the volume of mixture that has to be replaced by 10 liters of water = 41x

[Note how we are choosing the values so that we can avoid complicated fractions]

In 41x liters mixture,

Quantity of acid = 21x liters

Quantity of water = 20x liters

∴ Final quantity of acid = (84 – 21x) liters

∴ Final quantity of water = (80 – 20x + 10) liters = (90 - 20x) liters

ATQ,

(84 – 21x)/ (90 - 20x) = ¼

⇒ 336 – 84x = 90 – 20x

⇒ x = 246/64 = 123/32

∴ Quantity of mixture to be replaced = 123/32 × 41 = 157.6 liters