A few weeks prior to the CBT-CAT exam, two CAT aspirants, Roshni and Ketaki, decided to study together at Ketaki’s house. Ketaki studied Quant while Roshni tried to brush up her Verbal acumen. Suddenly, due to a storm in their area, the electricity went off and the town was engulfed in darkness. It was exactly midnight then. An eerie tune started playing. Suddenly, out of nowhere, a ghost glided into the room carrying a handful of candles. She introduced herself as "Vandana - The ghost of CAT Past". She told them her sad story of how she died giving CAT year after year without any preparation whatsoever and reminded them that it was now time to burn the midnight oil with CBT-CAT just around 3 months away.
She gave the girls a candle each. Both candles were equally long and were uniform throughout. However, the one she gave Ketaki was twice as thick as the one she gave Roshni. She told them that the thinner of the two candles could last 3 hours while the thicker one could last two hours longer. The light given off by the two candles together was bright enough to light up the entire room. She spent some time discussing the new format of the CBT-CAT and reminded them that the CAT advertisement will be released on Sunday, August 30 in all the leading newspapers. She wished them all the best and left at 1 am with the rest of the candles saying that they were for the other CAT aspirants she would be visiting that night. Before leaving, with a SNAP of her fingers, she lit the two candles and told the girls to start studying. After studying for some time, the girls got tired and extinguished the 2 candles together and fell asleep. When they woke up in the morning, Roshni’s candle's length was one-third that of Ketaki’s. At what time had they slept? Provide a detailed explanation along with your answer.