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

Let there be n bees in the swarm.
Kadamba: n/5
Silihindra: n/3
Kutaja: 3(n/3 - n/5)
Remaining = n - n/5 - n/3 - 3(n/3 - n/5)
1 = n - n/5 - n/3 - 3(n/3 - n/5)
Now, we solve this equation:
1 = n - n/5 - n/3 - n + 3n/5
1 = 3n/5 - 8n/15
1 = (9n - 8n)/15
n = 15
There are 15 bees in the swarm.