The correct answer is option 1, which states that only statement 1 is correct. Let`s dissect each statement to understand why.

Statement 1: Daylight varies throughout the year on the Earth. It varies the least at the Equator and the most at the Poles. This statement is true. Due to the Earth`s tilt on its axis and its elliptical orbit around the Sun, different parts of the Earth receive varying amounts of daylight throughout the year. The equator, being the closest to the Sun, experiences relatively consistent amounts of daylight throughout the year, while the poles can have extreme variations in daylight duration, with long summers of continuous daylight and long winters of continuous darkness.

Statement 2: From the total radiation of the Sun, only around 15 percent reaches the Earth`s surface. This statement is incorrect. Approximately 30 percent of the Sun`s radiation is reflected back into space by clouds, the atmosphere, and the Earth`s surface. The remaining 70 percent is absorbed by the Earth`s surface, causing it to heat up and radiate heat back into the atmosphere.

In conclusion, option 1 is the correct answer as only statement 1 is true.