Question

In the battle of Mahabharat Veer Arjun destroyed all the 125 raths (horse- carts). Out of which few were driven by 3 horses each and rest were driven by 5 horses each. Thus, he captured 125 damaged raths along with 575 horses. The raths which were driven by 5 horses belonged to the Kaurav and the raths which were driven by 3 horses belonged to the allied army of Kaurav. It is known that no any horse was injured in the bactle. The number of raths originally belonged to the Kaurav (not to their allied army) is : (a) 60 (b) 25 (c) 75 (d) 100

Short answer

Answer: 100 raths.

Step-by-step solution

Set up the equations

Let x be the number of raths driven by 3 horses (allied army) and y be the number of raths driven by 5 horses (Kaurav). Since the total number of raths is 125, we can write the first equation: x + y = 125 Next, we know that there were 575 horses captured. We get the second equation: 3x + 5y = 575

Solve the system of equations

We can use substitution or elimination to solve the system of equations. Here, we'll use substitution: From the first equation, we can express x in terms of y: x = 125 - y Substitute this expression for x in the second equation: 3(125 - y) + 5y = 575

Simplify the equation and solve for y

Simplify the equation: 375 - 3y + 5y = 575 Combine the coefficients of y: 2y = 200 Solve for y: y = 100

Find x using the value of y

Now that we know the value of y, we can plug it back into the equation for x: x = 125 - 100 x = 25

Answer the question

The number of raths originally belonging to the Kaurav, which were driven by 5 horses each, is y = 100. Therefore, the correct answer is (d) 100.

Key concepts

Algebra

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. It is a unifying thread of almost all of mathematics and includes everything from solving elementary equations to the study of the abstractions such as groups, rings, and fields. In the context of the given exercise, algebra is used to represent the problem of counting the raths and horses through a system of equations. These equations are a cornerstone of algebra and encode the information provided in the problem into a mathematical format.By translating a word problem into algebraic equations, one can harness the power of mathematics to find answers that are not immediately obvious. This approach is not only systematic but also a reliable way to tackle quantitative problems across diverse topics.

Linear Equations

Linear equations are fundamental to algebra, and they represent relationships where the variables involved do not have any exponents other than 1. A linear equation in two variables, such as the ones seen in the Mahabharat rath exercise, can be graphically represented as a straight line on a two-dimensional plane.

Formulating Linear Equations

A key skill in solving word problems is setting up the correct linear equations based on the given information. In our case, the equations are formulated to represent the total number of raths and the total number of horses. Understanding how to translate words into equations is a vital step in using algebra to solve problems.Solving linear equations often involves finding the value of the variables that make the equation true. The solutions to the equations represent the possible amounts of raths driven by 3 horses and 5 horses, which is essential to answer the question posed in the problem.

Word Problems

Word problems combine language and mathematics, challenging students to translate text into mathematical equations. The Mahabharat rath problem is an example, calling for an analytical approach to transform a narrative into algebraic expressions and then solve them.

Steps to Tackle Word Problems

• Read the problem carefully and determine what is being asked.
• Identify and assign variables to unknown quantities.
• Translate the words into algebraic expressions and equations.
• Use appropriate mathematical methods to solve these equations.
• Interpret the results in the context of the original problem.

By following these steps, students can convert the often intimidating text of word problems into solvable mathematical puzzles. Each word and phrase can provide clues about the operations and relationships between the quantities involved.

Quantitative Aptitude

Quantitative aptitude refers to the ability to handle numerical and mathematical calculations. This skill is essential in various academic fields, competitive exams, and real-life problem-solving. In the provided exercise, quantitative aptitude is demonstrated through the comprehension of the problem's context, formulation of algebraic equations, and the application of arithmetic to find the solution.

Enhancing Quantitative Aptitude

• Practice different types of mathematical problems to become familiar with a variety of concepts and techniques.
• Develop a step-by-step approach to solving problems, which helps in organizing thoughts and reducing errors.
• Work on improving mental math skills for quick calculations.
• Understanding that practice and familiarity with concepts will build speed and accuracy.

The ability to efficiently solve systems of equations, as seen in the Rath problem, is an example of applying quantitative aptitude. A strong foundation in algebra, linear equations, and solving word problems contributes to its development.