Question

Mr. Gupta divides Rs 81000 among his three children Ashok, mohit and Geeta in such a way that Ashok gets four times what Mohit gets and Mohit gets 2.5 times what Geeta gets. Find the share of each of them.

Answer 1

Hint: From the information given in the question, it is clear that Geeta gets the least share among the three children of Mr. Gupta. Therefore, we will assume a variable for Geeta’s share and then determine the shares of Mohit and Ashok respectively in terms of that variable. Now by addition of shares of all their children, we get the total amount which Mr. Gupta divides. Thus, we will get a linear equation and by solving it we can first find Geeta’s share and then accordingly Mohit’s and Ashok’s share respectively.

Complete step-by-step answer:
In the question, it is given that Mr. Gupta divides Rs 81000 among his three children Ashok, Mohit and Geeta in such a way that Ashok gets four times what Mohit and Mohit gets 2.5 times what Geeta gets.
From this it is clear that Geeta gets the smallest share among these three.
Let the share of Geeta be $ x $ Rupees.
Now, we will consider Mohit’s share. It is given that Mohit gets 2.5 times what Geeta gets.
Therefore Mohit gets $ 2.5x $ Rupees.
Finally for Ashok, it is given that he gets four times what Mohit gets.
Therefore, the share of ashok is: $ 4 \times 2.5x = 10x $ Rupees.
We know that the total of everyone’s share will be 81000 Rupees.
 $
   \Rightarrow x + 2.5x + 10x = 81000 \\
   \Rightarrow 13.5x = 81000 \\
   \Rightarrow \dfrac{{135}}{{10}}x = 81000 \\
   \Rightarrow x = \dfrac{{81000 \times 10}}{{135}} \\
   \Rightarrow x = 6000 \;
  $
Thus, Geeta gets 6000 Rupees.
Mohits gets $ 2.5x = 2.5 \times 6000 = 15000 $ Rupees.
Ashok gets $ 10x = 10 \times 6000 = 60000 $ Rupees.
So, the correct answer is “ 6000,15000 and 60000 ”.

Note: In this type of question, we should always remember to start the solution by assuming the variable value for the smallest quantity. For example, here we have identified from the given information that Geeta gets the least amount. After that we solved the problem by assuming Geeta’s share and determining shares of the other two with respect to it.