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The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. How much litres of water should be added? I. In a milk solution of 15 litres, milk and water are in the ratio 4 ∶ 1. II. When we add water, the ratio of milk to water in the solution becomes 3 ∶ 2. III. The ratio of milk to water will be 1 ∶ 5, when the water is excessive in the solution.

The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. How much litres of water should be added? I. In a milk solution of 15 litres, milk and water are in the ratio 4 ∶ 1. II. When we add water, the ratio of milk to water in the solution becomes 3 ∶ 2. III. The ratio of milk to water will be 1 ∶ 5, when the water is excessive in the solution. Correct Answer Statement I and Either statement II or statement III are required to answer the question.

Considering statement I and II together,

I. In a milk solution of 15 litres, milk and water are in the ratio 4 ∶ 1

II. When we add water, the ratio of milk to water in the solution becomes 3 ∶ 2

⇒ Quantity of Milk in the initial solution = (4/5) × 15 = 12 litres

⇒ Quantity of Water = 15 – 12 = 3 litres

Let x litres of water be added to the above solution to make the ratio 3 ∶ 2

⇒ 12/(3 + x) = 3/2

⇒ x = 5

⇒ The statements I and II together are sufficient to answer the question.

Considering statement II and III together,

II. When we add water, the ratio of milk to water in the solution becomes 3 ∶ 2

III. The ratio of milk to water will be 1 ∶ 5 when the water is excessive in the solution

⇒ The statement II and III are not sufficient together

Considering statements I and III together,

I. In a milk solution of 15 litres, milk and water are in the ratio 4 ∶ 1.

III. The ratio of milk to water will be 1 ∶ 5, when the water is excessive in the solution

Quantity of Milk in the initial solution = (4/5) × 15 = 12 litres

Quantity of Water = 15 – 12 = 3 litres

When water is excessive in the solution, the ratio will be 1 ∶ 5

⇒ 12/(3 + x) = 1/5

⇒ x = 57

⇒ The statements I and III are sufficient together

∴ Statement I and Either statement II or statement III are required to answer the question.

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