Finding Ankita's Brother's Weight: A Step-by-Step Solution

This problem involves calculating weights based on given relationships and percentages. We need to find the weight of Ankita's brother by first determining the weights of other family members.

Step 1: Determine the Weight of Ankita's Grandmother's Husband

The problem states the weight of Ankita's grandmother's husband directly.

• Grandmother's husband's weight = 81 kg

This is our starting point for calculating the other weights.

Step 2: Calculate the Weight of Ankita's Grandmother

We are told that Ankita's grandmother weighs 26 kg less than her husband.

Using the husband's weight from Step 1:

Grandmother's weight = Grandmother's husband's weight - 26 kg

\begin{equation*} \text{Grandmother's weight} = 81 \text{ kg} - 26 \text{ kg} \end{equation*}

\begin{equation*} \text{Grandmother's weight} = 55 \text{ kg} \end{equation*}

So, Ankita's grandmother weighs 55 kg.

Step 3: Calculate Ankita's Weight

The question states that Ankita's weight is 20% less than that of her grandmother. We calculated the grandmother's weight in Step 2.

First, let's find 20% of the grandmother's weight:

20% of 55 kg = \(\frac{20}{100} \times 55\)

\begin{equation*} \frac{20}{100} \times 55 = \frac{1}{5} \times 55 = \frac{55}{5} = 11 \text{ kg} \end{equation*}

Now, subtract this amount from the grandmother's weight to find Ankita's weight:

Ankita's weight = Grandmother's weight - (20% of Grandmother's weight)

\begin{equation*} \text{Ankita's weight} = 55 \text{ kg} - 11 \text{ kg} \end{equation*}

\begin{equation*} \text{Ankita's weight} = 44 \text{ kg} \end{equation*}

Ankita weighs 44 kg.

Step 4: Calculate the Weight of Ankita's Brother

Finally, we are told that Ankita's brother is 8 kg heavier than Ankita. We found Ankita's weight in Step 3.

Ankita's brother's weight = Ankita's weight + 8 kg

\begin{equation*} \text{Brother's weight} = 44 \text{ kg} + 8 \text{ kg} \end{equation*}

\begin{equation*} \text{Brother's weight} = 52 \text{ kg} \end{equation*}

The weight of Ankita's brother is 52 kg.

Summary of Weights

Based on the calculations, Ankita's brother weighs 52 kg.

Revision Table: Understanding Weight Calculations

Additional Information: Percentage Basics and Applications

Percentages are a way to represent a part of a whole as a fraction of 100. The word "percent" means "out of one hundred".

• A percentage can be written as a decimal or a fraction. For example, 20% is equivalent to 0.20 or \(\frac{20}{100} = \frac{1}{5}\).
• To find a percentage of a number, you multiply the number by the percentage expressed as a decimal or fraction.
• Problems involving "percentage less than" or "percentage more than" require calculating the percentage amount first and then subtracting it from or adding it to the original amount.
• These types of percentage problems are common in various real-life scenarios, such as calculating discounts, taxes, interest, and changes in values.

Understanding how to calculate percentages and apply them to scenarios like weight differences is crucial for solving many quantitative problems.