116 ms is the correct answer.
think it this way.. all the packets are transferred in pipeline. so find the transmission time of all the packets at the source which is 5*1000B/1Mbps=40ms.
now while the 5th packets is getting tranfered, remaining packets would be on theiir way, so we need to find the propagation delay and delays at the 2 switches only for the last packet.. which is 20*3ms=60ms(propagation delay through link)+ 2*1000*8/1Mbps=16ms(transmission delay at 2 switches)
summing up all= 40ms+60ms+16ms=116ms
compare with the answer you posted.. both are same.