Question

The average weight of 20, four wheelers is \(180 \mathrm{~kg}\). If an old car is removed from this group of four wheelers, the new average weight decreases by \(2 \mathrm{~kg}\). The weight of the removed car is : (a) 220 (b) 218 (c) 182 (d) none of these

Short answer

Answer: The weight of the removed four-wheeler is 218 kg.

Step-by-step solution

Calculate the initial total weight of the four-wheelers

In order to calculate the total weight of the 20 four-wheelers, we can use the formula: Total Weight = Average Weight × Number of Four-Wheelers Total Weight = (180 kg) × (20 four-wheelers) = 3600 kg

Calculate the new average weight after the car was removed

We are given that the new average weight decreases by 2 kg after the car was removed. Therefore, we can calculate the new average weight as: New Average Weight = 180 kg - 2 kg = 178 kg

Calculate the total weight of the remaining four-wheelers

To find the total weight of the remaining four-wheelers, we can use the same formula from Step 1 and the remaining number of four-wheelers after the old car was removed. Since one car was removed, there are now 19 four-wheelers. So, Total Weight = (New Average Weight) × (Remaining Number of Four-Wheelers) Total Weight = (178 kg) × (19 four-wheelers) = 3382 kg

Calculate the weight of the removed car

We can now calculate the weight of the removed car by subtracting the total weight of the remaining four-wheelers from the initial total weight of the four-wheelers: Weight of Removed Car = Initial Total Weight - Remaining Total Weight Weight of Removed Car = 3600 kg - 3382 kg = 218 kg The weight of the removed car is 218 kg, which corresponds to option (b).

Key concepts

Quantitative Aptitude

Quantitative aptitude encompasses the ability to understand and manage numerical data. It frequently involves using mathematical skills to solve real-world problems, such as calculating averages or comparing weights. In educational settings, developing a strong quantitative aptitude is crucial as it forms the basis for more complex mathematical reasoning and problem-solving.

For instance, when facing a question like the average weight calculation of vehicles, it's not just about finding a number but also understanding how that number is representative of a collective measure. In the given problem, the challenge was to adjust the average weight calculation after removing an item from the dataset - an aspect of problem-solving that taps into determined quantitative abilities.

Arithmetic Mean

The arithmetic mean, often referred to as the average, is a measure that is used to find the central tendency of a data set. It's calculated by adding all the numbers in the set together and then dividing by the count of numbers.

In the context of our problem, the initial average weight of the four wheelers is computed by dividing the total weight by the number of vehicles. Understanding how to adjust this mean when a data point (in our case, a car) is removed is essential. It showcases the direct relationship between the sum of all data points and the number of data points in calculating the mean.

Algebraic Problem Solving

Algebraic problem solving is a key aspect of mathematics that involves forming equations and finding unknowns based on the given information. It requires an understanding of both the arithmetic operations and the capability to represent real-life situations with algebraic expressions.

The exercise highlighted the use of simple algebra to deduce the weight of the removed car. By setting up an equation based on the total weighted average before and after the car's removal, and then solving for the unknown, students can find the precise weight of the removed car. This practical application of algebraic principles is core to problem-solving across various mathematical contexts.

Weight Comparison

Weight comparison is a critical skill that allows individuals to evaluate the difference in mass between objects or data sets. In practical terms, it might involve determining how much heavier or lighter one object is compared to another.

In our exercise, comparing the total weight before and after the car was removed provided the necessary insight to solve the problem. Through comparison, it becomes clear that the weight of the removed car is equivalent to the reduction in total weight, thus utilizing comparative judgment to reach a logical conclusion. Students learn not only to compute but also to interpret the significance of weight changes within a given context.