Question

How will Rs. 31500 be shared between A, B and C. If A gets the double of what B gets and B gets the double of what C gets?

Answer 1

Hint: We first assume the amount for C and then take the amount for B and A. We add them and equate with 31500 to form the equation. We solve that to find the value of $x$ and the rest of the values.

Complete step-by-step solution:
Rs. 31500 be shared between A, B and C such that A gets the double of what B gets and B gets the double of what C gets.
Let us assume that C gets Rs. $x$.
Now B gets the double of what C gets. So, B gets Rs. $2x$.
Again, A gets the double of what B gets. So, A gets Rs. $2x\times 2=4x$.
In total they get $x+2x+4x=7x$.
The total amount of money is Rs. 31500.
We equate that with $7x$ to get $7x=31500$.
We divide both sides with 7 to get
\[\begin{align}
  & \dfrac{7x}{7}=\dfrac{31500}{7} \\
 & \Rightarrow x=4500 \\
\end{align}\]
Therefore, C gets Rs. 4500. B gets $4500\times 2=9000$ Rs. and A gets $9000\times 2=18000$ Rs.
The division for A, B, C of the amount will be $18000,9000,4500$ respectively.

Note: We can also start the assumption of variables for A but in that case the amount for B and C becomes fraction. So, not to complicate the problem with more calculation we took the base assumption for C.