Solubility of potassium chlorate(V) in 100g of water at 70ºC is 78g.
Our sample was dissolved in 200g of water. Therefore, 136g of potassium chlorate(V) should have been dissolved.
However, we only added 80g. So, the full sample would have been dissolved.
So far: 80g of potassium chlorate(V) has fully dissolved in 200g of water.
Now, the solution becomes saturated when 80g of the potassium chlorate(V) dissolves in 200g of water.
Dividing by 2, solution becomes saturated when 40g of potassium chlorate(V) dissolves in 100g of water.
From the graph, we can see that this happens at 46ºC.
We know that solution was cooled to 20ºC from the question. Solubility per 100g of water at this temperature = 27g
Decrease in solubility (from 46ºC to 20ºC ) = 40-27 = 13g per 100g water
Since our solution was had 200g water, we multiply 13 by 2 to get 26g.