Question

The average value of property of Mittal, Ambani and Singhania is Rs. 11111 crore. The property of Singhania is as less as the property of Mittal is greater than the average property of both the Singhania and Mittal. The value of property of Ambani is : (a) Rs. 111 crore (b) Rs. 11111 crore (c) Rs. \(3703.7\) crore (d) can't be determined

Short answer

Answer: The value of Ambani's property can't be determined from the given information.

Step-by-step solution

Understanding the problem

First, let's represent the property values of Mittal, Ambani, and Singhania as M, A, and S respectively. We can begin by writing an equation about the average value of their properties.

Write the equation for average property value

The average value of the property of Mittal, Ambani and Singhania is given as Rs. 11111 crore. We can write this as an equation: \((M + A + S)/3 = 11111\)

Analyze the given condition about Singhania's and Mittal's properties

The property of Singhania (S) is as less as the property of Mittal (M) is greater than the average property of both Singhania and Mittal. Let x represent this difference. We can write two equations based on this information: 1. \(S = M - x\) 2. \(M = (S + M)/2 + x\)

Solve for x

We can solve for x using equations from step 3. Rewrite equation 1 as \(M = S + x\) and substitute this into equation 2: \(S + x = (S + (S + x))/2 + x\) Solve for x to get: \(x = 2S\)

Substitute and solve

Substitute the expression for x from step 4 into equation 1: \(S = (S + 2S) - 2S\) Therefore, \(S = S\), which means we cannot find a unique solution for S.

Substituting in the average equation

From Step 2, we have the average equation: \((M + A + S)/3 = 11111\) Substitute S for M from equation 1: \(((S + x) + A + S)/3 = 11111\)

Recognizing the limitation of given information

We can see that we have only one equation with two unknowns (A and S) and we cannot express one unknown in terms of the other. Therefore, it is not possible to find a unique value for A (Ambani's property). Hence, the answer is: (d) can't be determined

Key concepts

Average Value Calculation

The concept of averaging is a fundamental aspect of quantitative aptitude, particularly useful when we intend to find a central value that represents a collection of data points. In the context of the problem provided, the average value represents the equal distribution of property value between Mittal, Ambani, and Singhania. The formula for calculating the average value of 'n' numbers is \

\[ \frac{{\text{{Sum of all numbers}}}}{n} \]
For example, if the sum of the property values is Rs. 33333 crore for the three individuals, the average value for each, according to the formula, would be \

\[ \frac{{33333}}{3} = 11111 \]
Understanding this concept is crucial as it is not just about finding a simple mean, but it also often sets the stage for setting up algebraic expressions and equations, which leads to problem-solving in complex scenarios where values are unknown or indirectly given, as seen in the exercise.

Algebraic Expressions

Algebraic expressions are mathematical phrases that can contain ordinary numbers, variables (like x or y), and operators (like add, subtract, multiply, and divide). These expressions are like instructions that tell us what to do with numbers or variables. They become powerful tools when we solve problems involving unknown quantities.

In our example, we created algebraic expressions to represent the property values of Mittal (M), Ambani (A), and Singhania (S), and defined 'x' as the difference in property between Singhania and the average of Mittal and Singhania's properties. This allowed us to outline relationships and set up equations. By mastering algebraic expressions, one can translate word problems into solvable mathematical equations.

System of Equations

A system of equations is a collection of two or more equations with the same set of unknowns. Solving a system of equations requires finding the values of the unknowns that satisfy all the equations simultaneously. There are various methods to solve a system, like substitution, elimination, or using matrices.

In the exercise, we encounter an apparent system of equations initially. However, upon closer examination, we discover there is only one true equation with two variables, \

\[ (M + A + S)/3 = 11111 \]
and another equation that becomes an identity after manipulations, rendering it unhelpful for solving the problem. This demonstrates an important aspect of systems of equations: the need for at least as many independent equations as there are variables to obtain a unique solution. Without that, as shown in the exercise, we’re unable to conclusively solve for the individual properties of Ambani or Singhania, and the correct answer must be that it ‘can't be determined’.