The first building has been rebuilt, but the second, taller one is still present, alive and functioning in the same location.
Answer: The picture is of Rajaji Salai. The first building is the (in)famous Arbuthnot Bank whose collapse IN 1906 almost bankrupted entire South India. The Second building is now occupied by HSBC Bank.
The crash of Arbuthnot bank is an interesting study. When it crashed in 1906 it had dubious assets worth 7 million Pounds and liabilities of 27 million Pounds (and we are taking in 1906 values).
The firm invested lavishly in daring enterprises, such as searching for gold in the Nilgiris and Anamalais, investing in American railway projects and new South African goldfields, and in the plantation crops of the West Indies, amongst other ventures
History was to repeat itself when the successor to Arbuthnot Bank, the Indian Bank went through the same set of sequences in 1990s under the flamboyant chairman M. Gopalakrishnan lending recklessly to various ventures and almost folded.
Looks like Finance Company debacles are regular events of Madras History.
Futher details here. I guess this is an article by Mr. Muthiah, the tone is his, but there is no byline to the story.