The correct answer is (c), 1924.
The Indian Civil Service (ICS) was the elite civil service of British India. It was established in 1858, after the Indian Rebellion of 1857, and was responsible for the administration of British India. The ICS was a highly competitive service, and entry was by examination. The examination was held in England, and only British subjects were eligible to sit for it.
In the early 20th century, there was a growing demand for Indians to be allowed to sit for the ICS examination. This demand was met in 1924, when the British Government finally agreed to hold the examination simultaneously in India and England. This was a major step forward in the Indian independence movement, as it allowed Indians to compete for the highest positions in the Indian government.
The other options are incorrect. Option (a), 1922, is incorrect because the British Government did not agree to hold the ICS examination simultaneously in India and England in that year. Option (b), 1923, is incorrect for the same reason. Option (d), 1925, is incorrect because the British Government agreed to hold the ICS examination simultaneously in India and England in 1924, not 1925.