Answer

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**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.

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