Question

An incentive amount of Rs 58000 was divided among three sales persons Lovleen, Ankita, and Arun. Lovleen got 80 percent of what Ankita got and Ankita got 25 percent of what Arun got. Find the amount that each sales person got. Also find what percentage of the incentive amount that Ankita received.

Answer 1

Hint: Here first we will assume the share of Arun to be x and then we will form the linear equation in one variable with the help of given information and then solve them to get the value of x and then get the desired answers.

Complete step-by-step answer:
Let the share of Arun to be x and then it is given that Ankita got 25 percentage of what Arun got
Therefore, the share of Ankita is given by:-
\[{\text{Ankita's share}} = x \times \dfrac{{25}}{{100}}\]
Simplifying it we get:-
$ \Rightarrow$\[{\text{Ankita's share}} = \dfrac{x}{4}\] Rs.
Now it is given that . Lovleen got 80 percent of what Ankita got.
Hence, the share of Lovleen is given by:-
$ \Rightarrow$\[{\text{Lovleen's share}} = \dfrac{x}{4} \times \dfrac{{80}}{{100}}\]
Simplifying it we get:-
$ \Rightarrow$\[{\text{Lovleen's share}} = \dfrac{x}{5}\]Rs.
Now it is given that the total incentive amount is Rs 58000
Therefore, this implies that the sum of shares of each person is equal to Rs 58000.
i.e.
$ \Rightarrow$\[\dfrac{x}{5} + \dfrac{x}{4} + x = 58000\]
Taking LCM we get:-
$ \Rightarrow$\[\dfrac{{4x + 5x + 20x}}{{20}} = 58000\]
Solving it further we get:-
$ \Rightarrow$\[\dfrac{{29x}}{{20}} = 58000\]
Solving for the value of x we get:-
$ \Rightarrow$\[x = \dfrac{{58000 \times 20}}{{29}}\]
$ \Rightarrow$\[x = 40,000\]Rs.
Hence the share of Arun is Rs. 40000
Share of Ankita is \[\dfrac{{40,000}}{4}\]
                            = \[10,000\]Rs.
Share of Lovleen is \[\dfrac{{40,000}}{5}\]
                                = \[8000\]Rs.
Now we know that,
\[{\text{Percentage of incentives received}} = \dfrac{{{\text{amount received}}}}{{{\text{total amount}}}} \times 100\]
Hence, the percentage incentives received by Ankita is given by:
\[{\text{Percentage of incentives received}} = \dfrac{{10000}}{{{\text{58000}}}} \times 100\]
Simplifying it we get:-

\[{\text{Percentage of incentives received}} = 17.24\% \]

Note: Students should note that the linear equation in one variable has only one variable with highest power 1 while the linear equation in two variables has two variables each with highest power as 1.