Maths Formulas - life oriented mathematics

Maths Formulas - life oriented mathematics

PROFIT & LOSS :

* Gain = Selling Price(S.P.) – Cost Price(C.P)
* Loss = C.P. – S.P.
* Gain % = Gain * 100 / C.P.
* Loss % = Loss * 100 / C.P.
* S.P. = (100+Gain%)/100*C.P.
* S.P. = (100-Loss%)/100*C.P.
* If CP(x), Gain(y), Gain%(z). Then y = x*z/100.
[Same in case of Loss]

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# RATIO & PROPORTIONS:

* The ratio a : b represents a fraction a/b. a is
called antecedent and b is called consequent.
The equality of two different ratios is called
proportion.

* If a : b = c : d then a, b, c, d are in proportion.

* This is represented by a : b :: c : d.
In a : b = c : d, then we have a* d = b * c.
If a/b = c/d then ( a + b ) / ( a – b ) = ( c + d ) /
( c – d ).

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# TIME & WORK :

* If A can do a piece of work in n days, then A’s 1
day’s work = 1/n
* If A and B work together for n days, then (A+B)’s
1 days’s work = 1/n
* If A is twice as good workman as B, then ratio
of work done by A and B = 2:1

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# PIPES & CISTERNS :

* If a pipe can fill a tank in x hours, then part of
tank filled in one hour = 1/x
* If a pipe can empty a full tank in y hours, then
part emptied in one hour = 1/y
* If a pipe can fill a tank in x hours, and another
pipe can empty the full tank in y hours, then on
opening both the pipes,
* the net part filled in 1 hour = (1/x-1/y) if y>x
* the net part emptied in 1 hour = (1/y-1/x) if x>y

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# TIME & DISTANCE :

* Distance = Speed * Time
* 1 km/hr = 5/18 m/sec
* 1 m/sec = 18/5 km/hr
* Suppose a man covers a certain distance at x
kmph and an equal distance at y kmph. Then,
the average speed during the whole journey is
2xy/(x+y) kmph.

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# PROBLEMS ON TRAINS :

* Time taken by a train x metres long in passing a
signal post or a pole or a standing man is equal
to the time taken by the train to cover x metres.

* Time taken by a train x metres long in passing a
stationary object of length y metres is equal to
the time taken by the train to cover x+y metres.

* Suppose two trains are moving in the same
direction at u kmph and v kmph such that u>v,
then their relative speed = u-v kmph.

* If two trains of length x km and y km are moving
in the same direction at u kmph and v kmph,
where u>v, then time taken by the faster train to
cross the slower train = (x+y)/(u-v) hours.

* Suppose two trains are moving in opposite
directions at u kmph and v kmph. Then, their
relative speed = (u+v) kmph.

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

* If two trains start at the same time from two
points A and B towards each other and after
crossing they take a and b hours in reaching B
and A respectively, then A’s speed : B’s speed =
(√b : √a)

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# SIMPLE & COMPOUND INTERESTS :

Let P be the principal, R be the interest rate
percent per annum, and N be the time period.
* Simple Interest = (P*N*R)/100
* Compound Interest = P(1 + R/100)^N – P
* Amount = Principal + Interest
* when rate of interest time n principal are
constant den principal=(C.I.-S.I.)*(100/R)^N
* The Difference between C.I & S.I
For 2 Years = P(R/100)^2 = Difference
For 3 Years = [P (R/100)^2 ] × [(3+R/100)]

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LOGORITHMS :

If a^m = x , then m = loga(x).
Properties :
logx(x) = 1
logx(1) = 0
loga(x*y) = loga(x) + loga(y)
loga(x/y) = log ax – log ay
loga(x) = 1/logx(a)
loga(x^p) = p(loga(x))
loga(x) = logb(x)/logb(a)
Note : Logarithms for base 1 does not exist.