Understanding Weight Ratios and Sums

This problem involves understanding ratios and how to use them to find individual quantities when their sum is known. We are given the ratio of the weights of Jaya and Vijaya and their total combined weight. We need to find the specific weight of Vijaya.

Setting up the Ratio Problem

The ratio of Jaya's weight to Vijaya's weight is given as 4 : 5. This means that for every 4 units of weight Jaya has, Vijaya has 5 units of weight. We can represent their weights using a common multiplier, let's call it \(x\).

• Jaya's weight = \(4x\)
• Vijaya's weight = \(5x\)

Using the Sum of Weights

We are told that the sum of their weights is 72 kg. We can write this as an equation:

\(\text{Jaya's weight} + \text{Vijaya's weight} = \text{Total weight}\)

\(4x + 5x = 72\)

Solving for the Multiplier \(x\)

Now, we need to solve the equation for \(x\). Combine the terms on the left side:

\(9x = 72\)

To find \(x\), divide both sides of the equation by 9:

\(x = \frac{72}{9}\)

\(x = 8\)

So, the value of the multiplier \(x\) is 8.

Calculating Vijaya's Weight

We represented Vijaya's weight as \(5x\). Now substitute the value of \(x\) we found into this expression:

\(\text{Vijaya's weight} = 5x\)

\(\text{Vijaya's weight} = 5 \times 8\)

\(\text{Vijaya's weight} = 40\)

Therefore, Vijaya's weight is 40 kg.

Verifying the Solution

Let's check if the weights match the given information. If \(x=8\):

• Jaya's weight = \(4x = 4 \times 8 = 32\) kg
• Vijaya's weight = \(5x = 5 \times 8 = 40\) kg

The sum of their weights is \(32 \text{ kg} + 40 \text{ kg} = 72 \text{ kg}\), which matches the given total weight. The ratio of their weights is \(32 : 40\). Dividing both numbers by 8, we get \(4 : 5\), which also matches the given ratio.

The calculated weight of Vijaya is 40 kg.

Revision Table: Weight Ratio Calculation

Additional Information: Understanding Ratios

A ratio is a comparison of two or more numbers that indicates their relative sizes. In this problem, the ratio 4 : 5 means that for every 4 units of Jaya's weight, there are 5 units of Vijaya's weight. Ratios can be simplified like fractions. If the actual weights were 8 kg and 10 kg, the ratio would be 8:10, which simplifies to 4:5 by dividing both numbers by 2.

When a ratio represents parts of a whole (like weights contributing to a total sum), the sum of the ratio parts (4 + 5 = 9) corresponds to the total quantity (72 kg). Each 'part' of the ratio then corresponds to \(72 \text{ kg} / 9 = 8 \text{ kg}\). This is another way to think about the multiplier \(x\). If one part is 8 kg, then Jaya's 4 parts are \(4 \times 8 = 32\) kg, and Vijaya's 5 parts are \(5 \times 8 = 40\) kg.