A mountain range has 200 active volcanoes. In a particular year, 20% of the volcanoes exploded in the first two months, 40% of the remaining exploded by the half of the year, and at the end of the year, another 50% of the volcanoes that hadn't already erupted also exploded. How many mountains are still intact at the end of the year? Let's answer step by step:
By the first two months, 20 / 100 * 200 = 40 mountains had erupted. The total number of mountains remaining after the first round of explosions is 200 - 40 = 160. When 40% of the remaining mountains exploded, the number of mountains that were still intact decreased by 40 / 100 * 160 = 64. The number of mountains that hadn't exploded after the second explosions is 160 - 64 = 96. When 50% of the mountains which were still intact exploded, the number of mountains that hadn't erupted was reduced by 50 / 100 * 96 = 48. At the end of the year, 96 - 48 = 48 mountains remained intact and hadn't exploded. The answer: 48.