STOCK AND SHARES

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)

CALENDERS

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.

BANKERS DISCOUNT

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))]}

TRUE DISCOUNTS

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

CLOCKS

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)

NUMBER SERIES

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

PIPES AND CISTERNS

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)]

MENSURATIONS

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+b2 Þb = Öd2-l2 Þl = 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 = AT 2Pr(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 (3)Circumference,c = l+2r (23)Four circular carboard pieces,each of radius 'r'cm are placed in such a way that each piece touches two other pieces.The area of the space enclosed by four pieces is, (2r)2 [1-P/4]cm2 (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 (6) A1/A2 = (v1/v2)2/3 28.Area of four walls = 2 * (length + breadth) * height

PROFIT AND LOSS

PROFIT AND LOSS

1. Profit = S.P - C.P 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

AGES

AGES

No seperate formulas,But problems are done by logical method. Each part = Total Age/Sum of ratio's of Age's

RATIO AND PROPORTION

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

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)]

SIMPLIFICATIONS

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.

DECIMAL FRACTIONS

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 ]

L.C.M AND H.C.F

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 ]

ALLIGATION AND MIXTURES

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 ]

 

 

TIME AND WORK

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) ]

COMPOUND INTEREST

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 ]

AVERAGES

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) ]

DISCOUNTS

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 ]

SIMPLE INTEREST

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]