business mathematics

(1) Time taken by a train x mt long in passing a signal post or a pole or a standing man = time taken by the train to cover x mt.


(2) Time taken by a train x mt long in passing a stationary object of length y mt = time taken by the train to cover x+y mt.


(3) Suppose two trains or two bodies are moving in the same direction at u kmph and v kmph such that u > v then their relative speed is u-v kmph.


(4)If two trains of length x km and y km are moving in opposite directions at u kmph and v kmph,then time taken by the train to cross each other = (x+y)/(u+v) hr


(5) Suppose two trains or two bodies are moving in opposite direction at u kmph and v kmph then,their relative speed = (u+v) kmph


(6)If two train start at the same time from 2 points A & B towards each other and after crossing they take a & b hours in reaching B & A respectively then
A's speed : B's speed = (b^1/2 : a^1/2 )

Alligation or Mixtures Concept important points:

1.Alligation:
It is the rule that enables us to find the ratio in which two of more ingredients at the given price must be mixed to produce a mixture of a desired price.


2.Mean Price:
The cost price of a unit quantity of the mixture is called the mean price.


3.Rule of Alligation:
If two ingredients are mixed then
Quantity of Cheaper / Quantity of Dearer = (C.P of Dearer – Mean Price) /(Mean Price–C.P of Cheaper).


C.P of a unit quantity of cheaper(c)
C.P of unit quantity of dearer(d)


Mean Price(m)

(d-m) (m-c)

Cheaper quantity:Dearer quantity = (d-m):(m-c)


4.Suppose a container contains x units of liquid from which y units are taken out and replaced by water. After n operations the quantity of pure liquid = x (1 – y/x)n units.

Partnership:
When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.


Ratio of Division of Gains:

1.When the investments of all the partners are do the same time, the gain or loss is distributed among the partners in the ratio of their investments.

Suppose A and B invest Rs x and Rs y respectively for a year in a business, then at the end of the year: (A's share of profit):(B's share of profit)=x:y


2.When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital*number of units of time). Now gain or loss is divided in the ratio of these capitals.


Suppose A invests Rs x for p months and B invests Rs y for q months, then (A's share of profit):(B's share of profit)=xp:yq


3.Working and sleeping partners:A partner who manages the business is known as working partner and the one who simply invests the money is a sleeping partner.

Formula:

1.When investments of A and B are Rs x and Rs y for a year in a business ,then at the end of the year (A's share of profit):(B's share of profit)=x:y

2.When A invests Rs x for p months and B invests Rs y for q months, then
A's share profit:B's share of profit=xp:yq