A small island has $\frac{2}{5}$ of its surface covered by forest and $\frac{1}{4}$ of the remainder of its surface by sand dunes. The island also has 90 hectares covered by farm land. If the island is made up of only forest, sand dunes and farm land, what is the total area of the island, to the nearest hectare?
(A) 163
(B) 120
(C) 200
(D) 138
(E) 257
A small island has $\frac{2}{5}$ of its surface covered by forest and $\frac{1}{4}$ of the remainder of its surface by sand dunes. The island also has 90 hectares covered by farm land. If the island is made up of only forest, sand dunes and farm land, what is the total area of the island, to the nearest hectare?
(A) 163
(B) 120
(C) 200
(D) 138
(E) 257

## Solution

If $\frac{2}{5}$ of an island is covered by forest then $\frac{3}{5}$ of the island is made up of sand dunes and farm land.

Since $\frac{1}{4} \times \frac{3}{5}=\frac{3}{20}$ is made up of sand dunes this implies that $\frac{2}{5}+\frac{3}{20}=\frac{11}{20}$ of the island is made up of forest and sand dunes. Thus $\frac{9}{20}$ of the island, or 90 hectares, is made up of farm land.

Thus, the island must be $\frac{20}{\bar{x}_{1}}=9 Q$ or 200 hectares in total.

ANSWER: (C)