Veto q&a 7 Month22 (1)

Q& A Wallpaper
Dileep r.
average
• Average =
Sum of Observations
Number of Observations
n + 1
• Average of first ‘n’ Natural Numbers =
2
• Average of first ‘n’ Odd Numbers = n
• Average of first ‘n’ Even Numbers = n + 1
SuM Of firSt ‘N’ NuMBerS
n( n+ 1)
• Sum of first ‘n’ Natural Numbers =
2
• Sum of the squares of first ‘n’ Natural Numbers
n( n+ 1)( 2n+
1)
=
6
• Sum of the cubes of first ‘n’ Natural Numbers
2
⎡ n( n+ 1)
⎤
= ⎢ ⎥
⎣ 2 ⎦
• Sum of the first ‘n’ Whole Numbers =
n n−
1
• Number of shakehands =
2
• Sum of first ‘n’ Odd Numbers = n 2
• Sum of first ‘n’ Even Numbers = n(n+1)
PerceNtage
y
• y% of x = x × 100
y z
• z% of y% of x = x × ×
100 100
• If x% of a Number = y,
y
then the Number = ×100
x
• If x% of a Number = y,
y
then its z% = × z
x
( )
ratiO aND PrOPOrtiON
• a : b =
a
b
• If a : b = c : d then
a x d = b x c
• If a, b, c are in proportion then
a : b = b : c
• If xA = yB = zC then
a : B : c = 1 : 1 :
1
x y z
1 1 1
• : : = A : B : C then,
x y z
1 1 1
x : y : z = : :
A B C
A B C
• If = = then
x y z
a : B : c = x : y : z
SiMPle aND cOMPOuND iNtereSt
PNR
• Simple Interest, I =
100
N
⎛100
+ R ⎞
• Annual Compound Interest = P⎜
⎟ − P
⎝ 100 ⎠
2N
⎛ R ⎞
⎜100
+ ⎟
• Half yearly Compound Interest = P 2
⎜ ⎟ − P
⎜ 100 ⎟
⎝ ⎠
4N
⎛ R ⎞
⎜100
+
4
⎟
• Quarterly Compound Interest = P⎜
⎟ − P
⎜ 100 ⎟
⎝ ⎠
• The difference between Compound and Simple
Interest for 2 years for a particular amount ‘P’
2
⎛ R ⎞
= P ⎜ ⎟
⎝100
⎠
PrOfit aND lOSS
• Gain = Selling Price - Cost Price
Gain × 100
• Gain % =
Cost Price
100 + Gain% • Selling Price =
x Cost Price
100
100
• Cost Price =
x selling price
100 + Gain%
• Loss = Cost Price - Selling Price
Loss × 100
• Loss % =
Cost Price
−
= 100 Loss
• Selling Price
% x Cost Price
100
100
• Cost Price =
x Selling Price
100 − Loss%
WOrk aND tiMe
• If A can do a piece of work in ‘n’ days, then A’s
one day’s work =
1
n
• If A can do a piece of work in ‘a’ days and B can
do the same work in ‘b’ days, then both A and B
ab
together can finish the work in days
a+
b
• If A and B can together finish a job in ‘a’ days and
B alone can finish the same job in ‘b’ days, then,
ab
A alone can finish the job in days
a−
b
• If A can finish a work in ‘a’ days, B can finish
it in ‘b’ days and C can finish it in ‘c’ days
then A, B & C together can finish the work
abc
i n
days
ab + bc + ac
• If A men or B women can finish a work in C days,
then ‘a’men and ‘b’ women can finish the same
ABC
work in days
Ab + Ba
PiPeS aND ciSterN
• Pipe A can fill the tank in ‘a’ hours where as pipe
B can fill the tank in ‘b’ hours, if both the pipes
ab
are opened together the tank will be filled
in hours
a+
b
• Pipe A can fill the tank in ‘a’ hours where as pipe
B can empty the tank in ‘b’ hours, if both the pipes
ab
are opened together, the tank will be filled
in hours
a−
b
SPeeD, DiStaNce aND tiMe
Dis tance
• Speed =
Time
• If A and B covers equal distance at different
speeds ‘a km/hr’ and ‘b km/hr’ respectively then
2ab
the Average Speed =
a + b
⎛ 5 ⎞
• x km/hr = ⎜x
× ⎟m/sec
⎝ 18 ⎠
⎛ 18 ⎞
• x m/sec = ⎜x
× ⎟ km/hr
⎝ 5 ⎠
relative SPeeD
• If two bodies moves in the same direction with
speeds S1 and S2 then Relative Speed = S1 - S2
• If two bodies moves in the opposite direction with
speeds S1 and S2 then Relative Speed = S1+ S2
traiN
• If two trains of lengths L1 and L2 are moving in
opposite directions at speeds S1 and S2, then the
time taken by the trains to cross each other
L1+
L2
=
S1+
S2
• If two trains of lengths L1 and L2 are moving in
same directions at speeds S1 and S2, then the
time taken by the faster train to cross the slower
L1+
L2
train =
S − S
1 2
BOatS aND StreaMS
• In water, the direction along the stream is called
down stream and the direction against the
stream is called upstream
• If the speed of a boat in still water is ‘a km/hr’ and
the speed of the stream is ‘b km/hr’, then
Speed of downstream = (a+b) km/hr
Speed of upstream
= (a-b) km/hr
• If the speed of downstream is ‘x km/hr’ and that
of upstream is ‘y km/hr’, then
x + y
Speed of Boat in still water = km/hr
2
x − y
Speed of stream = km/hr
2
Q&AUbdn curreNt affairS & gk
March 2018