Hemant - Gajanan Cevian Theorem

Angle Divider Theorem©®
Refer attachments

New method of dividing a number by 7, when a number is divisible by 7

Short cut method of dividing by 7 when a number is divisible by 7.
This method is based on divisibility test for 7.
When a number passes this test , use the calculation done to find the quotient.
1) Calculate quotient for last step.
2) For a step, add the subtracted number and the right-most digit for that step.
3) Write this addition below quotient in first step such that only one digit comes extra at the right.
4) Repeat the steps 2) and 3) till you reach the dividend (the number you wanted to divide by 7).

http://mathandmultimedia.com/2012/02/29/divisibility-by-7-and-its-proof/

Application of Proability

There are 2 adjacent bus stops. A person A wants to reach a particular place by travelling by bus. For the destination, buses of 3 routes stop at 1st stop and bus of 1 route stops at other stop. Distance between 2 bus stops is 120 feet, At what distance should A stand from 1st bus stop.

Solution:
Total no. of bus routes for the particular destination = 4.
Buses of no. of bus routes stooping at 1st stop = 3
Therefore, Probability that A will get bus from 1st stop is 3/4.
{Had there been no bus stopping at 2nd bus stop for his destination he would have stopped at 1st bus stop only.}
He should stand nearer to 1st bus stop. So distance from 1st stop will be = (1-3/4)*120=  (1/4)*120 =30 feet from 1st bus stop.