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A shopkeeper has two types of rice having the rates of 50 per kg and 30 per kg. He mixed both types such that by selling the mixture at 49.5 per kg, there may be a gain of 10 percent. Find the ratio in which both types of rice are mixed.

A shopkeeper has two types of rice having the rates of 50 per kg and 30 per kg. He mixed both types such that by selling the mixture at 49.5 per kg, there may be a gain of 10 percent. Find the ratio in which both types of rice are mixed. Correct Answer 3 : 1

Given:

The selling price of the mixture = 49.5 per kg

Profit percentage = 10 percent

Rate of the first type of rice = 50 per kg

Rate of the second type of rice = 30 per kg

Formula used:

Profit percent = (Profit/Cost price) × 100

Calculation:

Cost price of the mixture = 49.5 ×

⇒ 49.5 × 100/110 = 45 per kg

Let the quantity of the first type of rice be x

Let the quantity of the second type of rice be y

(50 × x) + (30 × y) = 45 × (x + y)

⇒ 50x + 30y = 45x + 45y

⇒ 50x – 45x = 45y – 30y

⇒ 5x = 15y

⇒ x = 3y

⇒ x : y = 3 : 1

∴ The ratio in which both types of rice mixed is 3 : 1.

⇒ 49.5 × 100/110 = 45 per kg

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∴ The ratio in which both types of rice mixed is 3 : 1.

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