I read story that Ramakrishna said that he would once again take birth after 100 years or 200 years. Is it recorded in detail in any of the authentic biographies?
It is mentioned in Gospel of Sri Ramakrishna and Sri Ramakrishna The Great Master by Swami Sardananda
Gospel / Volume 2 / The Master On Himself And His Experiences:
Master - It will be sufficient for the youngsters who come here if they know only two things. If they know these, they will not have to practise much discipline and austerity. First, who I am, and second, who they are. Many of the youngsters belong to the inner circle. Those belonging to the inner circle will not attain liberation. I shall have to assume a human body again, in a northwesterly direction.
Part 2 - As The Spiritual Aspirant / Epilogue To The Story Of The Master's Sadhanas:
Pointing to the north-western direction, he told us over and over again that he would have to come to that region on the next occasion. Some assert that he gave them the time of his next advent and said, "I shall have to come to that side in two hundred years. Many will be liberated then. Those who do not get liberation at that time, will have to wait very long for it thereafter."