A plot of land is divided among three children. The first child receives one third of the land. The second child receives one half of what is left after the first child. The third child receives the remaining 200 square metres. What is the total area of the land?

Step-by-step solution

1. 1

   Give the unknown total a name. Let

   $x=\text{total area in square metres}$

   Every share will now be expressed as a fraction of $x$, which is what makes the final equation a one-liner.

2. 2

   Compute what is left after the first child. The first child takes $\tfrac13 x$, so the remainder is

   $x-\frac13x=\frac{3}{3}x-\frac13x=\frac23x$

3. 3

   Take the second child's share of the remainder, not of the whole. This is the trap in the problem: the second child gets half of $\tfrac23x$, not half of $x$.

   $\frac12\times\frac23x=\frac{2}{6}x=\frac13x$

   Coincidentally this also equals a third of the land, which is why the split feels equal at the end.

4. 4

   Find the third child's share and set up the equation. The first two children have taken $\tfrac13x+\tfrac13x=\tfrac23x$, so

   $\text{third child}=x-\frac23x=\frac13x$

   and that share is given as $200\ \text{m}^2$:

   $\frac13x=200$

5. 5

   Solve and check the whole split.

   $x=600$

   Check: first child $\tfrac13(600)=200$, remainder $400$, second child $\tfrac12(400)=200$, third child $600-200-200=200$ $\checkmark$. All three shares are $200\ \text{m}^2$ and they sum to $600\ \text{m}^2$, so the answer is choice B, $600\ \text{m}^2$.