A container contains 40 litres of milk. From this container, 4 litres

1.	A container contains 40 litres of milk. From this container, 4 litres of milk was taken out and replaced by water. This process was repeated further three times. Then, to make the mixture 50 litres, milk vendor added 10 litres of milk and water in 3 ∶ 2. What percent of milk is in excess in the container over the ratio of milk to water 3 ∶ 2?1). 17.4%2). 18.4%3). 20%4). 19%
Answer» Amount of milk left in the container after four times extraction of 4 liters of milk ⇒ [40{1 – (4/40)}⁴], ⇒ [40{1 – 0.1}⁴], ⇒ [40 {0.9}⁴], ⇒ [40 × 0.6561], ⇒ 26.244 liters ⇒ Amount of WATER in the container = 40 – 26.244 = 13.756 litres Now, 10 liters of the mixture is also added to make the quantity of mixture 50 liters ⇒ Quantity of milk to be added = 3/5 of 10 = 30/5 = 6 litres ⇒ Quantity of water to be added = 2/5 of 10 = 20/5 = 4 litres ⇒ TOTAL quantity of milk in mixture = 26.244 + 6 = 32.244 litres ⇒ Total quantity of water in mixture = 13.756 + 4 = 17.756 litres Let us assume that the quantity of water is 1 liter We need the quantity of milk as 1.5 liters to make the ratio of milk to water 3 ? 2 If 1 = 17.756 litres. Then, 1.5 = 17.756 × 1.5 = 26.634 litres It means that we need 26.634 liters of milk in the mixture. ⇒ Excess quantity of milk = 32.244 – 26.634 = 5.61 litres ⇒ Percentage of excess quantity of milk = (5.61 × 100)/32.244 = 17.4% ∴ 17.4% of milk is in excess over the ratio of milk to water 3 ? 2

A container contains 40 litres of milk. From this container, 4 litres of milk was taken out and replaced by water. This process was repeated further three times. Then, to make the mixture 50 litres, milk vendor added 10 litres of milk and water in 3 ∶ 2. What percent of milk is in excess in the container over the ratio of milk to water 3 ∶ 2?1). 17.4%2). 18.4%3). 20%4). 19%

Answer»

Amount of milk left in the container after four times extraction of 4 liters of milk

⇒ [40{1 – (4/40)}⁴],

⇒ [40{1 – 0.1}⁴],

⇒ [40 {0.9}⁴],

⇒ [40 × 0.6561],

⇒ 26.244 liters

⇒ Amount of WATER in the container = 40 – 26.244 = 13.756 litres

Now, 10 liters of the mixture is also added to make the quantity of mixture 50 liters

⇒ Quantity of milk to be added = 3/5 of 10 = 30/5 = 6 litres

⇒ Quantity of water to be added = 2/5 of 10 = 20/5 = 4 litres

⇒ TOTAL quantity of milk in mixture = 26.244 + 6 = 32.244 litres

⇒ Total quantity of water in mixture = 13.756 + 4 = 17.756 litres

Let us assume that the quantity of water is 1 liter

We need the quantity of milk as 1.5 liters to make the ratio of milk to water 3 ? 2

If 1 = 17.756 litres. Then, 1.5 = 17.756 × 1.5 = 26.634 litres

It means that we need 26.634 liters of milk in the mixture.

⇒ Excess quantity of milk = 32.244 – 26.634 = 5.61 litres

⇒ Percentage of excess quantity of milk = (5.61 × 100)/32.244 = 17.4%

∴ 17.4% of milk is in excess over the ratio of milk to water 3 ? 2