DISCOUNTS
1. [Gain = x-d-(x*d/100)]
x -----> Extra percentage added to C.P to fix
M.P
d -----> Discount offered on M.P
g -----> Gain% obtained
2. [Discount = M.P-S.P]
3. [d% = [ (M.P-S.P)/100] * 100 ]
4. [Discount = M.P * (d%/100)]
5. Successive Discounts,
[ D = (d1+d2)-(d1.d2)/100]
6. [ (C.P/M.P) = (100-d)/(100+g)]
7. [M.P=(S.P2-S.P1)/(d2-d1) * 100]
8. [S.P=M.P * (100-d)/100]
9. [S.P = M.P * [ (100-d1)/100 ] * [ (100-d2)/100 ] ]
10. Difference of discounts =
[M.P * [ d1.d2/(100*100) ] ]
11. [ [ (100-d1)/(100-d2) ] = [ (100+g1)/(100+g2) ] ]
12. Number of shirts = [ Total Discount/Discount on each shirt ]
13. [g% = [ (S.P-C.P)/C.P * 100 ] = [ (gain/C.P) * 100 ] ]
14. [C.P = (g/g%) * 100 ]
15. [S.P = (g/g%) * (100+g) ]
16. [C.P = [S.P/(100+g)] * 100 ]
17. [M.P = [C.P/(100-d)] * 100 ]
18. G = [ (G1+G2)+(G1.G2)/100]
19. [(100-d)(100+g * M.P ] = [S.P * (100)2]Þ
[(S.P/M.P) = [ (100-d) * (100+g) ]/(100)2 ]
-----------------------------------------------------------------------
-----------------------------------------------------------------------
-
L.C.M AND H.C.F
1. H.C.F of fractions =
[ H.C.F of Numerators/L.C.M of Denominators ]
2. (i)which will be divided - L.C.M
(ii)Which divides - H.C.F 3.The greatest number which can divide x, y
and z leaving the same remainder 'A' in each case is X-A = ?, Y-A = ?,
Z-A = ? and Find the H.C.F of obtained numbers. 4.The greatest number
by which if x and y are divided. The remainder will be A&B respectives
is, x.A = ? , y-B = ? Find the H.C.F of obtained numbers. 5.L.C.M of
fractions =
[ L.C.M of Numerators/H.C.F of Denominators ]
6. [ H.C.F * L.C.M = n1 * n2 ]
7. The least number which when divided by x,y and z leaves the
remainder A,B and C respectively is, x-A = ? , y-B = ? , z-C = ?. Here,
there will be equal difference between them i.e., D.
Required no = [ L.C.M of x,y and z ] - D
8. The smallest number which when diminished by A, is divisible by
p,q,r,s is,
Smallest no = [ (L.C.M of p,q,r,s) + A ]
-----------------------------------------------------------------------
-----------------------------------------------------------------
MENSURATIONS
1. Square:-figure
(1)Area = a2Sq units.
(or)
P2/16
(2) Perimeter = P =4a
(or)
a = P/4
(3) Digonal
(or)length of the rod that can be placed=
a = P/4
2. Rectangle:-figure
(1)Area =l*b
(2)Perimeter = P =2(l+b)
(3)Digonal =d = Öl2+b2Þb = Öd2-l2Þl = Öd2-b2
3. If area of plot is given as 'z'm2 and the
ratio of l:b is given as x:y, then length is
l = x * [Öz/(x*y)]
b = y * [Öz/(x*y)]
4. length required=(length * breadth of a room)/width of the carpet
5. No:of stones =(length * breadth of a room)/(length * breadth of a
stone)
6. A2/A1= (a2/a1)2 = (d2/d1)2
7. P2/P1=ÖA2/A1
8. Circle:-figure
(1)Area =Pr2 (or) P(d2/4)
(2)d = 2r
(3)Perimeter (or) Circumference =2Pr = Pd
Where P = 22/7 (or) 3.14
(4) A = c2/(4 P) (or) c = Ö4 PA = 2ÖPA
9. % dec in Area =fs [(r12 - r22)/r12] * 100
10. Distance travelled in 'N' revolutions is, D = N * Pd (or) N = D/(Pd)
11. Area left ungrazed =a2(1 - P/4)
12. Road out of the garden:-figure
(1)Area of the road =2w[l+b+2w] = [(l+2w)(b+2w)]-(l*b)
Road inside the garden:-figure
(2)Area of the road =2w[(l+b)-2w]
Two parallel roads:-figure
(3)Area of the road =w[(l+b)-w]
13.Traingles:-
(1)Right angled traingles:-figure
Area = (1/2)*b*h
d = Öb2+h2
(2)Equilateral traingles:-figure
Area=(Ö3/4)a2
Perimeter = P =3a
Height=(Ö3/2)a
(3)Scalene traingle:-figure
Perimeter = P =2s=a+b+c
Þs=(a+b+c)/2
Area = Ös(s-a)(s-b(s-c)
(4)Isosceles traingle:-figure
Perimeter = P =2a+b
Area =b/4(Ö4a2-b2)
14.Volumes:-
(a)Cube:-figure
(1)Lateral surface area =4a2
(2)Total surface area =6a2
(3)Volume of a solid = Base area * Height =a2 * a = a3
(4)Diagonal (or) Longest pole = d =Ö3a
(b)Cuboid:-figure
(1)Lateral surface area = AL =2h[l+b]
(2)Total surface area = AT 2[lb+lh+bh]
(3)Volume = V =lbh
(4)Diagonal = d =Öl2+b2+h2
(5)No:of boxes =(lbh)/l1b1h1 = (Volume of big box)/(Volume of small box)
15. a3 = v13+v23+v33
16. a1/a2 = (v1/v2)1/3
17. No:of boxes(if areas are given) =a3/a13 = (a/a1)3
(18) Cylinder:-figure
(1)Lateral surface area = AL =2Prh
(2)Total surface area = AT2Pr(h+r)
(3)AT/Al=(h+r)/h
(4)Volume = v =Pr2h
(5)Area of each flat surface i.e of ends =Pr2
(19) Cone:-figure
(1)Slant height = L =Öh2+r2
(2)Volume of the cone =1/3(Pr2h)
(3)Curved surface area of cone =Prl
(4)Total surface area =Pr(l+r)
(5)v1/v2=(r1/r2)2 * h1/h2
20. H-h = (4/3) * rs 3/rd2
21. Area of circle inscribed in an equilateral
traingle is r2.It's height is, h = 3r
(22) Sector:-figure
(1)l= (q/360)*2P r
(2)A =(q/360)*Pr2
(24) Rhombus:-figure
(1)4a2 = d12 + d22
(2)Area =(1/2)d1d2
(3)Perimeter = P =4a
(25) Parallelogram:-figure
(1)Area of DleABC 1/2(bh)
(2)Area of DleACD 1/2(b/h)
(3)Area of parallelogram =bh
(26) Trapezium:-figure
(1)Area of Trapezium=Area of (DleABC + DleACD)
1/2(ah) + 1/2(bh) = [(1/2)h][a + b]
(27) Sphere:-figure
(1)Surface area =4Pr2
(2)Volume =4/3(Pr3)
(3)A1/A2 = (r1/r2)2
(4)v1/v2 = (r1/r2)3
(5)v1/v2 = (A1/A2)3/2
-----------------------------------------------------------------
NUMBER SERIES
1. The difference between the no: and the no: obtained by interchanging
the digits is 'x'.The difference between digits is ,
diff = x/9
2. The sum of the no: and the no: obtained by interchanging the digits
is 'y'.The sum of the digits is ,
sum = y/11
3. The sum of two numbers is 'x' and their difference is 'y'.The product
of the no: is ,
[(x + y)2 - (x - y)2]/4
4. Dividend = (Divisor * Quotient) + Remainder
-----------------------------------------------------------------------
----------------------------------------------------------------------
PARTNERSHIP
1. Part of A/Part of B =
[(Amount invested by A*No.of months invested)/(Amount invested by
B*No.of months invested)]
2. Each part =(Total profit/Total of Ratios)
-----------------------------------------------------------------------
---------------------------------------------------
PERCENTAGES
1. If x% is deducted on tax and y% of the remaining is spent on
education and still there is a balance, the formula is :-
Balance * [ 100/(100-x) ] * [ 100/(100-y) ] * [ 100/(100-z) ]
2. The population of a town is 'P'. It increased by x% during Ist year,
increased by y% during IIst and again increased by z% during Ist. The
population after 3 years will be,
P * [ (100+x)/100 ] * [ (100+y)/y ] * [ (100+z)/100 ]
3. % of effect
(i) Inc of x% Dec of x% x-y-[(x*y)/100]
(ii) Inc of x% Inc of y% (x+y)+[(x*y)/100]
(iii) Dec of x% Inc of y% [-x2/100]
(iv) Dec of x% Dec of y% (-x-y)+[(x*y)/100]
(v) Inc of x% Dec of x% [-x2/100]
(vi) Inc of x% Inc of x% 2*x+[x2/100]
4. (i) If the sides of the traingle,rectangle,square,circle,rhombus etc
is increased by x%.Its area is increased by
2x+(x2/100)
(ii)If decreased x%.Its ares is decreased by,
-2x+(x2/100)
5. In an examination x% failed in Hindi and y% failed in Science, if z%
of the candidates failed in both of the subjects. The percentage of
students who passed in both of the subjects is,
100-(x+y-z)
6. If A's income is r% more than B's income, the B's income is less
than A's income by
(r/100+r) * 100%
7. If A's income is r% less than B's income, then B's income is more
than A's income by
(r/100-r) * 100
8. (i)If the price of comodity increases by r% then reduction in
consumption so as not to increase the expenditure is
(r/100+r) * 100
(ii)If the price of comodity decreases by r% then,
(r/100-r)*100
9. If the population of town (or) length of a tree is 'p' and its annual
increase is r% then,
(i)populaton (or) length of a tree after 'n' years is,
p[1+(r/100)]
(ii)population (or) length of a tree 'n' years ago is,
p/[1+(r/100)n]
10. If the population of town (or) value of a machine is 'p' and annual
decrease is r% then,
(i)populaton (or) value of machine after 'n' years is,
p[1-(r/100)n]
(ii)population (or) value of a machine 'n' years ago is,
p/[1-(r/100)n]
11. If 'A' is x% of 'C' and 'B' is y% of 'C' then 'A' is
(x/y) * 100%
of 'B'.
12. If two values are respectively x% and y% more than a third value,
then the first is
[(100+x) / (100+y)] * 100%
of second
13. Total no.of votes =
(Difference in votes/Difference in %) * 100
14. Maximum marks =
[(pass marks/pass %) * 100]
15.Total marks =
(Difference in marks / Difference in %)*100
16. (i)Reduced rate =
[(Amount/Quantity more) * (Reduction % /100)]
(ii)Original rate (or) previous rate =
[(Amount/Quantity more) * (Reduction % /100-reduction%)]
17. (i)Increased rate =
[(Amount/Quantity less) * (increase % /100)]
(ii)Original rate (or) previous rate =
[(Amount/Quantity less) * (Increase % /100-increase%)]
18. If the numeratorof fraction is increased by x% and its denominator
is diminished by y% ,the value of the fraction is A/B.Then the original
fraction is,
(A/B) * [(100-y) / (100+x)]
-----------------------------------------------------------------------
-------------------------------------------------------------------
PIPES AND CISTERNS
1.
t (A + B) = (tA * tB)/(tA + tB)
2.
tA = (tB * t (A + B))/(tB - t (A + B))
3.Time for filling , (Filling pipe is bigger in size.)
F = (e * f)/(e - f)
4.Time for emptying , (emptying pipe is bigger in size.)
E = (f * e)/(f - e)
5.
T(A + B + C)=L/[(L/tA) + (L/tB) + (L/tC)]
6.Pipes 'A' & 'B' can fill a tank in f1hrs & f2hrs respectively.Another
pipe 'C' can empty the full tank in 'e'hrs.If the three pipes are
opened simultaneously then the tank is filled in ,
F = L/[(L/f1) + (L/f2) - (L/e)]
7.Two taps 'A' & 'B' can fill a tank in 't1' & 't2' hrs
respectively.Another pipe 'C' can empty the full tank in 'e'hrs.If the
tank is full & all the three pipes are opened simultaneously . Then the
tank will be emptied in,
E = L/[(L/e) - (L/f1) - (L/f2)]
8.A filling tap can fill a tank in 'f'hrs.But it takes 'e'hrs longer
due to a leak at the bottom.The leak will empty the full tank in ,
E = [t(f * e) * tf]/[t(f + e) - tf]
9.Capacity of the tank is ,
F = (f * e)/(e - f)
10.
tc = [t(A + B) * t(A + B + C)]/[t(A + B) - t(A + B + C)]
11.
T = (xyz)/[(xz) + (yz) - (xy)]
-----------------------------------------------------------------------
----------------------------------------------------------------------
PROFIT AND LOSS
1. Profit = S.P - C.
2. Loss = C.P - S.P
3.Gain% = (Gain/C.P)*100
4.Loss% = (Loss/C.P)*100
5.S.P = [(100+Gain%)/100]*C.P
6.C.P=S.P*[100/(100+Gain%)]
7.S.P= [(100-Loss%)/100]*C.P
8.C.P= S.P*[100/(100-Loss%)]
9.By selling an article for Rs/ '-S'1 , a man looses 'L%'.In order to
gain 'G%' he uses the following formula,
S1/(100-L%)=S2(100-G%)
10.If C.P of 'x' articies is equal to the S.P of 'y' articles,the
profit% is:
[(x-y)/y]*100
11.Gain%=[Error/(truevalue-error)]*100
12.C.P = S.P/(1-losspart)
13.C.P=S.P*[100/(100+g1)]*[100/(100+g2)]*[100/(100+g3]
14.S.P=C.P*[(100+g1)/100]*[(100+g2)/100]*[(100+g3)/100]
15.C.P = [(S.P1-S.P2)/x2-x1]*100
x1 ---------> gain1 (or) loss1
x2 ---------> gain2 (or) loss2
16.S.P=C.P + [(C.P*g)/100]
17.Overall gain or loss =(x1*g1)-(x2*L1)+(x3*g3)
Where x1,x2,x3 ----------> Parts of items sold
-----------------------------------------------------------------------
-----------------------------------------------------------------
RATIO AND PROPORTION
1.If a:b = c:d , then Product of Means=Product of Extremes i.e
2ndterm*3rdterm=1stterm*4thterm
2.Each part =
Total Amount/Total of Ratios
3.If a:b = x:y & b:c = p:q ,then
a:b:c = xp:yp:yq
4.Third proportion to 'x' & 'y' =
y2/x
5.The mean proportion between 'a' & 'b' =
Öab
-----------------------------------------------------------------------
------------------------------------------------
SIMPLE INTEREST
1.S.I = PTR/100
P -----> Principal
T -----> Time (in yrs)
R -----> Rate % per anum
2.Amount = P+S.I
3.TO find the rate of interest per annum when a sum double/triple etc
itself in x years.Then,
[R * T = 100 * (n-1)]
4.[(R1*T1)/R2*T2) = (N1-1)/(N2-1)]
5.[(A/S.I = (100/R*T)+1]
6.[R(or)T = Ö(100*S.I)/P]
7.[(R1-R2) = (More interest * 100/(P*t))]
8.A=[(P+S.I) = P(1+(T.R/100))]
9.[P=(A1*T2-A2*T1)/T2-T1]
A ---> Amount
T ---> Time
10.R=[(A2-A1)/(A1*T2-A2*T1)] * 100
11.[I = ATR/(100+TR)]
12.If I1= I2,[(P1/P2) = (T2.R2)/T1.R1]
13.
[P = (100/Id)/(Rd.T)]
14.[T = (100.Id/Pd.R)]
15.[T = (100.Id/P R.d)]
16.[R = (100.Is/Td.P)]
17.[Gain = P.Rd.T/100]
18.[R = (100.ITotal)/(P1.T1+P2.T2+P3.T3)........]
19.[P=(100.ITotal/(R1.T1+R2.T2+R3.T3+......)]
20.a[ [100/100] + [(100+R)/100] + (100+2R)/100] + .......] = 0
a ---> Annual instalment.
D ---> Amount due
21. A = P * [ (100+R1+R2+R3)/100]
-----------------------------------------------------------------------
--------------------------------------------------
SIMPLIFICATIONS
1.V ---> - (Veruculum)
B ---> () (Bracket)
O ---> of (of)
D ---> % (division)
M ---> * (Multiplication)
A ---> + (Addition)
S ---> - (Subtraction)
In this chapter, we must simplify the problems in
the above order only
-----------------------------------------------------------------------
-----------------------------------------------------
STOCK AND SHARES
Formulae on Stock & Shares:-
1.No: of stock =
Total Stock/100
Purchase Cost / (Mk.Vl + BR)
Sale Realisation / (Mk.Vl - BR)
Annual Income/Rate%
Formulae on Debentures:-
2.No: of Share =
Investment (or) Purchase Cost/[MK.VL(1 + B%)]
Sale Realisation/[Mk.Vl(1 - B%)]
(Annual Income * 100)/(Divident% * Face value)
-----------------------------------------------------------------------
--------------------
TIME AND WORK
1.
tA+B = (tA * tB)/tA
2.
tB = (tA * tA+B)/tA - (tA+B)
3.
tA+B+C =[ L/(L/tA) + (L/tB) + (L/tC) ]
L ---> L.C.M of tA,tB,tC.
4.
tC =[ L/(L/tA+B+C) - (L/tB) - tB) ]
5.If A+B, B+C, A+C are given then A+B+C=?
(i)
tA+B+C = 2L/[ (L/tA+B) + (L/tB+C) + (L/tC+A) ]
(ii)
tC = 2L/[ (L/tB+C) + (L/tC+A) + (L/tA+B) ]
(iii)
tB = 2L/[ (L/tA+B) + (L/tB+C) + (L/tA+C) ]
6.
S1d1 = S2d2
7.
wA+B = [ (wA * wB)/(wA+wB) ]
8.Working alternatively,
2 * tA+B = 2 * [ (tA.tB)/(tA+tB) ]
-----------------------------------------------------------------------
------------------------------------------------------
TIME AND WORK
1.
tA+B = (tA * tB)/tA
2.
tB = (tA * tA+B)/tA - (tA+B)
3.
tA+B+C =[ L/(L/tA) + (L/tB) + (L/tC) ]
L ---> L.C.M of tA,tB,tC.
4.
tC =[ L/(L/tA+B+C) - (L/tB) - tB) ]
5.If A+B, B+C, A+C are given then A+B+C=?
(i)
tA+B+C = 2L/[ (L/tA+B) + (L/tB+C) + (L/tC+A) ]
(ii)
tC = 2L/[ (L/tB+C) + (L/tC+A) + (L/tA+B) ]
(iii)
tB = 2L/[ (L/tA+B) + (L/tB+C) + (L/tA+C) ]
6.
S1d1 = S2d2
7.
wA+B = [ (wA * wB)/(wA+wB) ]
8.Working alternatively,
2 * tA+B = 2 * [ (tA.tB)/(tA+tB) ]
-----------------------------------------------------------------------
-------------------------------------------------------------
TRUE DISCOUNTS
T.D -----------> True Discount
P.W -----------> Present Worth
S.I -----------> Simple Interest
A -----------> Amount
R -----------> Rate
T -----------> Time
1.
A = P.W + T.D
2.
P.W = (100 * amount)/[100 + (R * T)]
3.
T.D = (P.W * R * T)/100
4.
T.D = (A * R * T)/[100(R + T)]
5.
S.I on T.D = S.I - T.D
6.
sum = (S.I * T.D)/(S.I - T.D)
7.When the sum is put at C.I ,
P.W = A/[1 + (R/100)]T
8.
T.D = S.I on P.W
9.
P.W = (100 * T.D)/(R * T)
10.
T = (100 * T.D)/(P.W * R)
11.When the interest is at C.I ,
T.D = P.W[1+ (r/100)]t - P.W
-----------------------------------------------------------------------
-------------------------------------------------------------------
DECIMAL FRACTIONS
1.
[ (a2-b2)/(a+b) ] = [ a-b ]
2.
[ (a2-b2)/(a-b) ] = [ a+b ]
3.
[ (a3+b3)/(a2-(a*b)+b2) ] = [ a+b ]
4.
[ (a3-b3)/(a2-(a*b)+b2) ] = [ a-b ]
5.
[ (a+b)2+(a-b)2 /(a2+b2) ] = 2
6.
[ (a2+b2-(2*a*b) )/(a-b) ] = [ a-b ]
7.
[ (a2+b2+(2*a*b) )/(a+b) ] = [ a+b ]
-----------------------------------------------------------------------
---------------------------------------------------
COMPOUND INTEREST
1.
A = P [ 1 + [ R/(100*n) n*t] ]
P -----> Principle
R -----> Rate % per annum
n -----> No.of convertions per year
T -----> Time in years
2.C.I=A-P i.e.,
[ P [ 1+(R/(100*n)n*t] - 1 ]
3.When interest is calculated anually n=1,
A = P[1+(R/100)t]
4.When time is in fraction, t = x * (1/y) year:
A = P[1+(R/100)x] + [1 + (1/y)*R/100 ]
5.When rate od interest is R1% R2% R3% for Ist year,IIndyear,
IIIrd year respectively then amount,
A = P [ 1 + (R1100) * [1+(R2/100)] [1+(R3/100)]
6.When difference between C.I and S.I on certain sum at rate% on Rs.x,
[ C.I - S.I = sum * (r/100)2 ]
i.e., [ D = P * (r/100)2 ]
Note: Applicable only for two years.
7.
D =[ (P*R2)(300+R)/1003 ]
Note:Applicable only for 3 years.
8.
[ C.I/(200+R) = S.I/200 ]
Note: Applicable only for 2 years.
9.
R = [ (2*difference of C.I and S.I)/S.I ] * 100
10.R% amounts after 2 successive years we given:-
R = [ (An+1-An)/An ] * 100
An+1 -----> Amount after (n+1) years.
An -----> Amount after (n+1) years.
11.
P =[ A32/A6 ] =
[ A22/A4 ] =
[ A12/A2 ] =
[A42/A8 ]
Note: Double the years.
12.
P =[ A23/A32 ] =
[ A34/A43 ] =
[ A45/A54 ]
Note: Consecutive years.
P =[ ÖA23/A6 ] =
[ ÖA13/A3 ] =
[ ÖA33/A9 ]
13.
R =[( A6/A3)1/3 - 1 ] =
[ ( A4/A2 )1/2 - 1 ] =
[ ( A5/A2 )1/3 - 1 ]
R =[( A7/A2)1/3 - 1 ] =
[ ( A10/A2 )1/8 - 1 ] =
[ ( A10/A7 )1/3 - 1 ]
14.Installment problems:
a [ 100/(100+R) + 100/(100+R)2 + 100/(100+r)3 + ....... ] = B
a -----> Annual installment
B -----> Borrowed amount.
15.
R = [ (A/P)1/T - 1 ] * 100
16.
P = [ A2 * [100/(100+R)]2 ]
-----------------------------------------------------------------------
-----------------------------------------
CLOCKS
1.For coinciding the hands ,
(5x) * (12/11)
x -----> first given time.
2.Right angles at each other ,
(5x ± 15) * (12/11)
3.Opposite Direction ,
(5x - 30) * (12/11)
4.For finding time when it is 't'min space apart ,
(5x ±t) * (12/11)
5.For finding the angle between the hands of a clock is ,
30 * [HRS - (MIN/5)] + (MIN/2)
-----------------------------------------------------------------------
-------------------
CHAIN RULE
1.
M1D1T1S1W2 A2F2 = M2D2T2 S2W1A1F1
M -----> Men/labour
D -----> Days
T -----> Time (in hrs)
S -----> Speed
W -----> part of work done/wages
A -----> Amount earned
F -----> Food consumed/Milk used/coal required for
Machines/Diesel required for pumps.
2.D1W1 = D2W2
i.e.,
D1(L2B2H2) =
D2(L1B1H1)
D ---> Days
L ---> Length
B ---> Broad (or) Breadth
H ---> Deep
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CALENDERS
1. 100 years contains '5' odd days.
200 years contains '3' odd days.
300 years contains '1' odd days.
400 years contains '0' odd days.
2. Sunday -------> '0' odd day.
Monday -------> '1' odd day.
. .
. .
. .
3.One leap year contains '2' odd days.
4.The years which are mul of '4' are called leap years.
5.Leap year -------> 366 days (feb --> 29 days).
Ordinary year -------> 365 days.
6. MONTHS DAYS
Jan 31
Feb 28 (or) 29
Mar 31
Apr 30
May 31
Jun 30
Jul 31
Aug 31
Sep 30
Nov 30
Dec 31
7.One week = '7' days.
8.Leap year ------> '52' weeks + '2' odd days.
Ordinary year ------> '52' weeks + '1' odd day.
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BOATS AND STREAMS
b ---> Boat speed/Man speed in water.
c ---> Current Speed/Speed of the River.
d ---> Down stream speed.
u ---> Up stream speed.
D ---> Total distance travelled.
T ---> Total time.
1.
d=b+c
2.
u=b-c
3.
b=(d+u)/2
4.
c=(d-u)/2
5.Average Speed=(2xy)/x+y i.e
(b2-c2)/b
6.
D=[T(xy)]/x+y=[T(b2-c2)]/2b
7.
T=(D*2b)/b2-c2
8.
T=(D/d)+(D/u)=[D/(b+c)]+[D/(b-c)]
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BANKERS DISCOUNT
B.D -----------> Bankers Discount
S.I -----------> Simple Interest
T.D -----------> True Discount
B.G -----------> Bankers Gain
1.On bill for unexpired time ,
B.D = S.I
2.
B.G = B.D - T.D
3.
B.G = S.I on T.D
4.
T.D = Ö(P.W) * (B.G)
5.
B.g = (T.D)2/(P.W)
6.
B.D = (A * R * T)/100
7.
T.D = (A * R * T)/[100 + (R * T)]
8.
A = (B.D * T.D)/(B.D - T.D)
9.
T.D = (B.G * 100)/(R * T)
10.
Sum due = (B.D * T.D)/(B.D - T.D) = (B.D * T.D)/B.G Sum due = Amount
11.
T.D/B.G = Sum/B.D
12.
B.D - T.D = A * {(R + T)2/[100(100 + (R * T))]}
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AVERAGES
1.
Average = [ Total of observations/No.of observations ]
2.(i)When a person joins a group in case of increasing average Age
weight of new comer =
[ (Previous Age + No.of persons) * Increase in Avg ]
(ii)In case of decreasing Average, Age (or) weight of new comer =
[ (Previous Age - No.of persons) * Decrease in Avg ]
3.When a persom leaves a group and another person joins the group in
the place of person left, then
(i)In case of increasing average, Age (or) weight of new comer =
[ (Age of person left + No.of persons) * Increase in Avg ]
(ii)In case of decreasing Average, Age (or) weight of new comer =
[ (Age of person left - No.of persons) * Decrease in Avg ]
4.When a person leaves the group but no body joins this group, then
(i)In the case of increasing Average, Age (or) weight of man left =
[ (Previous Age - No.of present persons) * Increase in Avg ]
(ii)In case of decreasing Average, Age (or) weight of new comer =
[ (Previous Age + No.of present persons) * Decrease in Avg ]
5.If a person travels a distance at a speed of x Km/hr returns to the
original place of y Km/hr then average speed is
[ 2.x.y/(x+y) ]
6.If half of the journey is travelled at speed of x km/hr and the next
half at a speed of x km/hr. Then average speed during the whole journey
is
[ 2.x.y/(x+y) ]
7.If a person travels 3 equal distances at a speed of x Km/hr,
y Km/hr,z km/hr.Then average speed during whole journey is
[ 3.x.y/(x.y+y.x+z.x) ]
8.
A½
[ 3.x.y/(2x*y) ]
9.A½
[ 3*L/[ (L/S1)+(L/S2)+(L/S3) ]
10.A½
4L/[ (L.S1)+(L/S2)+L/S3)+(L/S4) ]
11.A½
1/[ (x/100) * (1/S1) ] + [y/100) * (1/S2) ] + [ (z/100)*(1/S3) ]
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ALLIGATION AND MIXTURES
1.
C.P = [ S.P/(100+g) * 100 ]
2.Mean rate of interest,
R = [ (100*I)/P*T) ]
3.Final % of Alcohol =
[ (Qi/Pi)/(Qi+Qw added) ]
Pi -----> Initial percentage
Qw -----> Quantity of water added
4.Final % of alcohol =
[ (Qi*Pi)/(Qi-Qw evoparated) ]
Qw -----> Quantity of water evoparated.
5.Quantity of water to be added =
[ Qmix * [(P2-P1)/(100-P2) ] ]
P1 and P2 are percentages of water.
6.Other than water =
[ Qmix * (P1-P2)/P2 ]
P1 and P2 are the % of constituent other than
water (i.e., salt,alcohol etc)
7.Ratio of water to milk =
g/100
8. Percentage of water =
[ (100*g)/(100+g) ]
9.
[ 1- (y/x) ]n * x
x -----> Capacity of container (or) Initial
quatity of pure milk.
y -----> Quantity drawn out each time.
n -----> No.of operations.
10.No.of rabits (4 legs) =
[ No.of legs given - (No.of heads given * 2) ]/2
No.of pigeons =
[ No.of heads given - No.of rabits ]
11. The mixture drawn out and replaced with water, so that the mixture
may be half water and milk is =
[ (1/2) * (difference in parts/greater part) ]
12.One gallon =
[ 100 litres ]
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AGES
No seperate formulas,But problems are done by logical method.
Each part = Total Age/Sum of ratio's of Age's
SHORTCUT METHODS FOR APTITUDE
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