How is 786 equal to Bismillah Rahmani Rahim? Find out

Many of us have used 786 to denote the basmallah but do we know how they number is related to it? I remember in my primary school days we always used to write 786 on top of the exam answer sheets to seek blessings and start the exam with Bismillah which is what we are supposed to do when doing something good. I have been intrigued by how the 786 came to equal bismillah. I just found out and thought may be someone else did not know like me. Here is how.
the Arabic letters were divided following a certain numerical values given to each of the consonants. i am sure you must have come across the following words which have no meaning themselves before you started the Quran proper.

:
	أبجد/ هوز/ حطي/ كلمن /سعفص/ قرشت/ ثخذ/ ضظغ

in the above arrangement, each of the consonant in the groups is allotted a specific number, viz

alif=1   baa=2   jeem=3   daal=4  haa=5     waaw=6   zaa=7  haa=8   taa=9  yaa=10
kaaf=20  laam=30  meem=40  noon=50  seen=60  'ayn=70  faa-80  saad=90  qaaf=100
raa=200  sheen=300  taa= 400  thaa=500  khaa=600  dhall=700  daa=800  zaa=900  ghayn= 1000 so
بسم الله الرحمن الرحيم will be baa=2  seen=60  meem=40  alif=1  laam=30  laam=30  haa=5  alif=1  laam=30  raa=200  haa=8  meem=40    noon=50  alif=1  laam=30  raa=200 haa=8  yaa=10  meem=40

if you sum up the numbers;
2+60+40+1+30+30+5+1+30+200+8+40+50+1+30+200+8+10+40=786

What I dont know yet is why the specific numbers were allotted to the specific letters ie why is raa equal to 200.
I am holding a key holder by one leading Muslim supplier of car windscreens and it has 786/110 inscribed on it. I am raking my head trying to see what the 110 stands for following the above numerical versus letter pattern.

now you know.