The Fruit Pricing Puzzle: Solving the Orange, Apple, and Banana Conundrum

Welcome to a unique and challenging puzzle involving fruit prices. We will walk you through a step-by-step guide to solve the complex relationships between the prices of pineapples, oranges, apples, and bananas, leading to the price of one banana.

Understanding the Problem

Our problem starts with a simple statement: 'For the price of one pineapple I will buy two oranges. For the price of three oranges I will buy four apples. I will buy six bananas for the price of three apples. What is the price of one banana if I pay 1 euro for one pineapple?' This riddle might seem complicated at first, but let's break it down and solve it logically.

Step-by-Step Solution

Step 1: Calculate the Price of One Orange

We start with the information that the price of one pineapple is 1 euro. The price of one pineapple is the price of two oranges: 1 euro 2 oranges. Therefore, the price of one orange is 0.50 euros.

Step 2: Calculate the Price of One Apple

We know that the price of three oranges (3 x 0.50 euros) is equal to the price of four apples. Thus, 1.50 euros 4 apples. The price of one apple is 0.375 euros.

Step 3: Calculate the Price of One Banana

We know that the price of three apples (3 x 0.375 euros) is equal to the price of six bananas. Thus, 1.125 euros 6 bananas. The price of one banana is 0.1875 euros.

Alternative Methods to Solve the Problem

Method 1: Using Fractions

Another way to solve this problem involves working with fractions to simplify the relationships between the fruits.

Firstly, we know two oranges cost 1 euro. Therefore, one orange costs 0.50 euros. Three oranges cost 1.50 euros (3 x 0.50 euros). Since four apples cost 1.50 euros, each apple costs 0.375 euros. Three apples cost 1.125 euros (3 x 0.375 euros). Since six bananas cost 1.125 euros, each banana costs 0.1875 euros.

Method 2: Direct Substitution

We can also use a more direct substitution method to solve the problem.

If one pineapple costs 1 euro and two oranges cost 1 euro, then the price of one orange is 0.50 euros. If three oranges cost 1.50 euros, then four apples cost 1.50 euros, making each apple 0.375 euros. If three apples cost 1.125 euros, then six bananas cost 1.125 euros, making each banana 0.1875 euros.

Conclusion

The price of one banana is 0.1875 euros. This solution is based on the relationships between the fruits and the given price of one pineapple. By breaking down the problem step-by-step, we can effectively solve the puzzle and determine the exact price of each fruit.

FAQ

What is the Relationship Between Pineapple and Orange?

The price of one pineapple is 1 euro, which is equal to 2 oranges. Therefore, the price of one orange is 0.50 euros.

What is the Relationship Between Orange and Apple?

Three oranges cost 1.50 euros (3 x 0.50 euros), and four apples cost 1.50 euros. Therefore, the price of one apple is 0.375 euros.

What is the Relationship Between Apple and Banana?

Three apples cost 1.125 euros (3 x 0.375 euros), and six bananas cost 1.125 euros. Therefore, the price of one banana is 0.1875 euros.