Question

out of a swarm of bees one fifth part settled on a kadamba blossom; one third on a silihindra flower; three times the difference of those numbers flew to the bloom of a kutaja. one bee, which remained, hovered about in the air. tell me, charming woman, the number of bees

Answer 1

setting things up:
let x be the # of bees in the swarm, then 
$\frac{x}{5}+\frac{x}{3}+3(\frac{x}{3}-\frac{x}{5})+1=x$

multiply across by 15
$3x+5x+3(5x-3x)+15=15x$
$8x+3(2x)+15=15x$
$8x+6x+15=15x$
$14x+15=15x$
$15=x\leftrightarrow x=15$