Chapter wise important Arithmetic Formulas
¬
SPEED ,DISTANCE AND TIMES
v
Speed = Distance ÷ Time
v
Time = Distance ÷ Speed
v
Distance = Speed × Time
v
Distance = Rate × Time
v
Rate =
Distance ÷ Time
v
Convert from Kph ( Km/hour)
to Mps (M/sec) : X km/hrs= X * 5/18 m/sec
v
Convert from Mps (M/sec) to
Kph (Km/hour) : x m/sec=
X * 18/5 km/sec
v
Suppose a man covers a
certain distance at X km/hr and an equal
distance at Y km/hr ,Then The average speed during the whole jouney is à 2xy ÷ (X+Y)
v
When speed is constant
distance covered by the object is directly proportional to the time taken, i.e à If Sa = Sb then Da
÷ Db = Ta ÷ Tb
v
When time is constant speed
is directly proportional to the distance travelled, i.e à Ta = Tb then Sa ÷ Sb = Da ÷ D
v
When Distance is constant
Speed is inversely proportional to the time taken i.e à If Da = Db then Sa ÷
Sb = Ta ÷ Tb
v If two objects are moving in same direction with speeds A and B then their relative speed
is à ( a – b )
v If two objects are moving is opposite direction with speeds A and B then their relative speed
is à ( a + b )
¬
AVERAGE
v Average à ( Sum of observations / Number of observations).
v If a person travels a distance at a speed of X km/hr and the same distance at a speed
of Y km/hr then the average speed during the whole
journey is given by Ã
2xy/x+y
v If the average age is decreased, age of new person
à Age of separate
person -
( Decrease in average × total
number of persons )
v If the average age is increased, age of new person à Age of separate person
+ ( Increase in average × total
nnumbeer of persons )
v When a person joins the group in Case of increase in average,
Age of new member à Previous average + (
Increase in average × Number
of members including new member)
v When a person joins the group In case of Decrease in average,
Age of new member à Previous average –
(Decrease in average × Number
of members including new member)
v In the Arithmetic Progression there are two cases when number
of terms is odd and second one is when number of terms is even.
I.
when the terms of the
numbers is odd the average will be-the
middle term.
II.
When the numbber of
terms is even then the average will be the average of two middle terms.
¬PERCENTAGE
v
If we have to convert percentage into fraction then it is
divided by 100.
v
If we have to convert fraction into percentage we have to
multiple with 100.
PERCENTAGE
|
FRACTION
|
DECIMAL
|
1%
|
1/100
|
0.01
|
5%
|
1/20
|
0.05
|
10%
|
1/10
|
0.1
|
15%
|
3/20
|
0.15
|
20%
|
1/5
|
0.2
|
25%
|
¼
|
0.25
|
30%
|
3/10
|
0.3
|
35%
|
7/20
|
0.35
|
40%
|
2/5
|
0.4
|
45%
|
9/20
|
0.45
|
50%
|
½
|
0.5
|
55%
|
11/20
|
0.55
|
60%
|
3/5
|
0.6
|
65%
|
13/20
|
0.65
|
70%
|
7/10
|
0.7
|
75%
|
¾
|
0.75
|
80%
|
4/5
|
0.8
|
85%
|
17/20
|
0.85
|
90%
|
9/10
|
0.9
|
95%
|
19/20
|
0.95
|
100%
|
1
|
1
|
Some of Important
Fraction Percentage
PERCENTAGE
|
FRACTION
|
DECIMAL
|
5 5/9
|
1/18
|
0.55556
|
6 ¼
|
1/16
|
0.0625
|
12 ½
|
1/8
|
0.125
|
16 2/3
|
1/6
|
0.166667
|
26 2/3
|
4/15
|
0.266667
|
33 1/3
|
1/3
|
0.33333
|
37 1/2
|
3/8
|
0.375
|
66 2/3
|
2/3
|
0.666667
|
v If the price of a commodity increases by R% then the
reduction in consumption so as not to increase the expenditure is à [ R/ (100+R)] × 100%
v If the price of a commodity decrease by R%, then the
increase in consumption so as not to decrease the expenditure is à [ R/ (100-R)] × 100%
v Let the population of a town be P now and suppose it
increases at the rate of R% per annum, then Ã
I.
The Population after (N)
years = P.( 1 + R/100)n
II.
The Population (N) years ago = P/( 1 + R/100)n
v Lets the present value of a machine be P. Supposed, it
depreciates.@ (at the rate of) R% per annum, then Ã
I.
Value of the machine
after n years = P( 1 – R/100)n
II.
Values of the machine (n) years
ago = P/[(1 – R/100)]n
III.
If A is R% more than B, then B is less than A by
= [R/ (100 + R)] × 100%
IV.
If A is R% less than B, then B is more than A by
= [R/ (100 - R)] × 100%
o Note : For two successive changes of x%
and y%, net change = {x + y + xy/100}%
¬PROFIT AND LOSS
v Cost Price is the
price at which an article is purchased, abbreviated as C.P ( cost price)
v Selling Price is the price at which an article is sold ,
abbreviated as S.P (Selling Price)
v If the Selling Price exceeds the Cost Price, then there is
Profit
v Profit Or gain à (S.P – C.P)
v Profit in percentage(%) Ã Profit/( C.P) × 100
v S.P Ã ( 100 + gain % )/ 100 × C.P
v C.P Ã 100/( 100 + gain % ) × S.P
v If the overall Cost Price exceeds the selling Price of the
buyer then he is said to have incurred loss.
v Loss à (C.P – S.P)
v Loss in percentage (%) Ã Loss/(C.P) ×
100
v S.P Ã ( 100 – loss % )/ 100 × C.P
v C.P Ã 100/( 100 – loss %) × S.P
v Profit and Loss Based on Cost Price (C.P)
I.
To find the percent
gain Or Loss , divided the amount gained or lost by the Cost Price &
multiply it by 100.
II.
To find the loss and
the selling price when the cost and the percent loss are given, multiply the
cost by the percent & subtract the product from the cost.
¬ Discount à M.P – S.P
¬ Discount %, D% Ã Discount/(MP) × 100
¬ PARTNERSHIP
v P1 : P2 Ã C1 × T1 : C2 : T2
v Here , P1 = Profit for Partner 1.
C1 = Capital by Partner 1.
Time-1 = Time period for which
Partner 1 invested his capital.
P2 = Profit for Partner 2
C2 = Capital by Partner 2.
Time-2 = Time period for which Partner 2
invested his capital.
¬ TIME , WORK & WAGES
v Work from days :
o
If A can
do a piece of work in n Days, Then A’s n day’s work is = 1/n
o
No. of days = Total
works / (works done in 1 day)
o
Days from work : If A’s
1 day’s work = 1/n then A can finish the work in n days.
v Relation between Men and
work :
o More Men
-------------- Can Do ---------------> More Work
o Less Men -------------- Can Do --------------->
Less Work.
v Relation Between Work and Time
o
More work ------------- Takes
-----------------> More Time
o
Less work
-------------- Takes -----------------> Less Time
v Relation Between Men And Time
o More men ------------ Can do in -------------> Less Time
o Less men
------------- Can do in -------------> More Time
v If M1 persons can do W1 work in D1 days and M2 persons can do
work in D2 days, then Ã
M1.D1/W1 = M2.D2/W2
v If M1 Persons can do W1 work in D1 days for H1 hours and M2
persons can do W2 work in D2 days for H2 hours , then
M1.D1.H1/W1 = M2.D2.H2/W2
v If A can do a work in ‘X’ days and A+B can do the same work in
‘Y’ days, then the number of days required to complete the work if A and B work
together is
X*Y/X+Y
v If A can do a work in ‘X’ days and A+B can do the same work in
‘Y’ days, then the number of days required to complete the work if B works
alone is
X*Y/X-Y
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