Introduction:

Solar year and Lunar year:

  The inimitability of the Noble Quran is confirmed by modern astronomy, indicating that the solar year is exactly 365.422 days. During this period of time, the earth completes its orbit around the sun, and the four seasons, summer, autumn, winter and spring take place. The lunar year is exactly 354.36780 days. This period of time is based on the length of time between two consecutive eclipses of the sun divided by the number of motions the moon travels around the earth. 

“And they stayed in their Cave three hundred (solar) years, adding nine”.

[ Al-Kahf,25 ]

  While interpreting "And they stayed in their Cave three hundred (solar) years and add nine (for lunar years)", Ibn Katheer said, "Allah means to inform His Messenger PBUH about the period of the time the people of the Cave spent in their Cave from the time Allah made them to sleep until He caused them to wake up and to be discovered by other people after 300 solar years but 309 years according to the lunar calendar. That is why after Allah the Almighty says 'And they stayed in their Cave three hundred (solar) years', He, Glory to Him, goes on to say 'and add nine (for lunar years)'."

 In Al-Jalalain book of Quranic interpretation we read: “adding nine”, i.e. nine years, for 300 Solar years make 309 Lunar years.
 To wrap up, Allah, Most Gracious, speaks the truth as He says,

(Verily, therein is indeed a reminder for him who has a heart or gives ear while he is heedful.)

[ [ Qaf, 37] ]