75 liters of kerosene oil and 25 liters of petrol are to be filled equally in a tank without mixing them. How many minimum tanks are needed and how many liters of oil are there in each tank?
The Correct Answer and Explanation is:
To determine the minimum number of tanks required to store the kerosene oil and petrol without mixing them, and how many liters of each liquid will go into each tank, we need to consider the capacity of each tank and the total amount of both liquids.
Step 1: Understanding the problem
- You have 75 liters of kerosene oil and 25 liters of petrol.
- You are tasked with filling these liquids equally in the tanks without mixing them.
- Each tank will contain either kerosene oil or petrol, but not both.
Step 2: Finding the number of tanks
To fill the liquids equally into the tanks, let’s assume you want each tank to be filled with a specific amount of liquid.
- For the kerosene oil, since there are 75 liters of it, the number of tanks required for kerosene oil will depend on how much you want in each tank. Let’s say each tank can hold the same amount of liquid. To divide 75 liters into tanks, you can consider the greatest common divisor (GCD) of 75 and 25 (since the two amounts must be divided without mixing), which is 25. This means: Each tank will contain 25 liters of kerosene oil. 7525=3 tanks for kerosene oil.\frac{75}{25} = 3 \text{ tanks for kerosene oil.}2575=3 tanks for kerosene oil.
- For the petrol, there are 25 liters, and if each tank is also holding 25 liters, you need: 2525=1 tank for petrol.\frac{25}{25} = 1 \text{ tank for petrol.}2525=1 tank for petrol.
Step 3: Conclusion
- You need a total of 4 tanks:
- 3 tanks for kerosene oil, each containing 25 liters.
- 1 tank for petrol, containing 25 liters.
This is the minimum number of tanks required to store the kerosene oil and petrol separately, ensuring there is no mixing between the two. Each tank holds exactly 25 liters of the respective liquid.
