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?
By the first two months, 20/100*200 = <<20/100*200=40>>40 mountains had erupted.
The total number of mountains remaining after the first round of explosions is 200-40= <<200-40=160>>160
When 40% of the remaining mountains exploded, the number of mountains that were still intact decreased by 40/100*160 = <<40/100*160=64>>64
The number of mountains that hadn't exploded after the second explosions is 160-64 = <<160-64=96>>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 = <<50/100*96=48>>48
At the end of the year, 96-48 = <<96-48=48>>48 mountains remained intact and hadn't exploded.
#### 48