Question

A shopkeeper has two types of a mixture of tea. In 48 kg of the first mixture ratio of tea to impurity is 5:3 and in 42 kg of the second mixture ratio of tea to impurity is 3 : 1. If the shopkeeper mixes these two mixtures with 56 kg of pure tea in a large container, then find the ratio of tea to impurity in the container?​

Answer 1

To find the ratio of tea to impurity in the container, add up the tea and impurity for each mixture and the pure tea. The ratio of tea to impurity in the container is 4.12 : 1.

Step-by-step explanation:

To find the ratio of tea to impurity in the container, we need to add up the tea and impurity from both mixtures and the pure tea. Let's calculate the total tea and impurity separately for each mixture:

In the first mixture, the total ratio of tea to impurity is 5 + 3 = 8. So, the total tea in the first mixture is (5/8) * 48 kg = 30 kg and the total impurity is (3/8) * 48 kg = 18 kg.

In the second mixture, the total ratio of tea to impurity is 3 + 1 = 4. So, the total tea in the second mixture is (3/4) * 42 kg = 31.5 kg and the total impurity is (1/4) * 42 kg = 10.5 kg.

Now, we add up the total tea and impurity from both mixtures and the pure tea: Total tea = 30 kg + 31.5 kg + 56 kg = 117.5 kg and Total impurity = 18 kg + 10.5 kg + 0 kg (pure tea has no impurity) = 28.5 kg. Therefore, the ratio of tea to impurity in the container is 117.5 kg : 28.5 kg, which can be simplified to 4.12 : 1.