Question

The average value of property of Agil, Mugilan and Anitha is $Rs.130$ crores. The property of Agil is $20$ crores greater than the property of Mugilan, and Anitha property value is $50$ crores greater than the Agil property value. What is the value of property Anitha?

Answer 1

In this question, we are given three different sentences giving us information about the value of 3 properties. First, form three different equations using the given information. Then, substitute and simplify these equations among themselves and find the value of the required property.

Complete step by step solution:
We are given certain sentences giving information regarding the value of 3 properties. Using these given sentences, we have to make the equations.
Let property Agil be denoted by $x$, property Mugilan be denoted by $y$ and property Anitha be denoted by $z$.
Now, we will make the equations.
It is given that the average value of property of Agil, Mugilan and Anitha is $Rs.130$ crores. Using the formula of mean, Mean $= \dfrac{{{\text{Sum of observations}}}}{{{\text{No}}{\text{. of observations}}}}$,
$\Rightarrow \dfrac{{x + y + z}}{3} = 130$
$\Rightarrow x + y + z = 390$ crores ……………….. (1)
Next line of the question is - The property of Agil is $20$ crores greater than the property of Mugilan.
$\Rightarrow x = \left( {y + 20} \right)$ crores
Shifting to find the value of $y$,
$\Rightarrow y = \left( {x - 20} \right)$ crores ……………... (2)
Next – Anitha property value is $50$ crores greater than the Agil property value.
$\Rightarrow z = \left( {x + 50} \right)$ crores ……………... (3)
We have to find the value of $z$.
Putting (2) and (3) in (1). This will give us an equation entirely in terms of $x$.
$\Rightarrow x + \left( {x - 20} \right) + \left( {x + 50} \right) = 390$ crores
Solving to find the value of x,
$\Rightarrow 3x - 30 = 390$ crores
$\Rightarrow 3x = 390 + 30 = 420$ crores
$\Rightarrow x = \dfrac{{420}}{3} = 140$ crores
Putting the value of $x$ in equation (3),
$\Rightarrow z = 140 + 50 = 190$ crores.

Therefore, the value of property Anitha is $190$ crores.

Note: It is always a smart move to divide the question into parts and mark the useful sentences. Otherwise, the useful information sometimes goes unnoticed. Then, extract the required information out of these sentences and use the method of substitution to find the value of the assumed variables.