Sandeep entered the last-16 after beating Lukas Dekys of the Czech Republic in his second-round bout. The Indian led throughout the bout and was unanimously declared the winner in all three rounds.
He will now square off against Japan's Goh Hasaka, who defeated Iraq's Jamal Hayder in his second-round bout.
Manjeet, on the other hand, fought hard against Rakhat Marzhikpayev of Kazakhstan but could not come through. The Indian gave his more fancied rival a tough time but eventually had to bow out, losing 1-2.
The mega-event is doubling up as a qualifying event for the Youth Olympics to be held in Nanjing, China from August 16 to 28.
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The youngsters, all in the age bracket of 17 and 18, will have to reach at least the semi-finals of the world event to make the cut for the Youth Olympics.
The Indians are competing under the International Boxing Association (AIBA) flag due to the termination of the Indian Boxing Federation following its failure to comply with the world body's directives on holding elections.