How to Divide Rs 65 in the Ratio of 2:3
Dividing a sum of Rs 65 in the ratio of 2:3 might seem like a complex mathematical problem, but it is a straightforward process once you break it down into simpler steps. We will explore several methods to resolve this problem and demonstrate the calculations involved.
Method 1: Using the Total Number of Parts
First, let's understand the total number of parts in the ratio. The ratio 2:3 consists of 2 parts (2) and 3 parts (3), making a total of 5 parts. This means:
2 3 5
Next, to find the value of each part, we divide the total amount (Rs 65) by the total number of parts (5).
Rs 65 ÷ 5 Rs 13
Now, using the value of each part, we can calculate the two portions of the division:
For 2 parts: 2 × Rs 13 Rs 26
For 3 parts: 3 × Rs 13 Rs 39
Method 2: Using Proportion and Proportion Solving
Alternatively, we can use proportions to divide the amount. The proportion can be set up as:
2:3 :: 65 : (2/5 × 65 | 3/5 × 65)
Upon evaluating and simplifying the proportion:
2:3 :: (2 × 13) : (3 × 13)
This gives us:
2:3 :: Rs 26 : Rs 39
Method 3: Solving the Equation
We can also solve this problem using algebra. Let's introduce a variable K where one part of the ratio (2 parts) is 2K and the other part (3 parts) is 3K. Therefore, the sum of these parts is:
2K 3K 65
Simplifying this, we get:
5K 65
Solving for K:
K 65 ÷ 5 13
Then, multiplying K by 2 and 3 to get the values of each part:
2 parts: 2 × 13 26
3 parts: 3 × 13 39
Thus, the division of Rs 65 in the ratio of 2:3 is Rs 26 and Rs 39.
Proof and Verification
To verify, we can check if the sum of Rs 26 and Rs 39 equals Rs 65:
26 39 65
This confirms that the division is correct.