SOME IMPORTANT FACTS & FORMULAE HELPFUL FOR SOLVING APTITUDE SECTION

TIME AND DISTANCE -> IMPORTANT FACTS AND FORMULAE :1. Speed = [Distance/Time],

Time=[Distance/Speed],

Distance = (SpeedxTime)2. x km/hr =

[xx 5/18]m/sec.3. If the ratio of the speeds of A and B is

a:b, then the ratio of the times taken by them to cover the same distance is1/a : 1/b orb:a.4. x m/sec = [x

x18/5] km/hr.5. Suppose a man covers a certain distance at

x km/hrand an equal distance aty km/hr. then, the average speed during the whole journey is[2xy/x+y] km/hr.

PROFIT AND LOSS -> IMPORTANT FACTS AND FORMULAE:

Cost Price: The price at which an article is purchased, is called its cost price, abbreviated as C.P.

Selling Price: The price at which an article is purchased, is called its cost price, abbreviated as C.P.

Profit or Gain: The price at which an article is purchased, is called its cost price, abbreviated as C.P.

Loss: If S.P is less than C.P., the seller is said to have incurred a loss.

1. Gain = (S.P.) – (C.P.)

2. Loss or gain is always reckoned on C.P.

3. gain% = [Gain*100/C.P.]

4. Loss = (C.P.) – (S.P.)

5. Loss% = [Loss*100/C.P.]

6. S.P. = (100+Gain%)/100 * C.P.

7. S.P. = (100-Loss%)/100 * C.P.

8. C.P. = 100/(100+Gain%) * S.P.

9. C.P. = 100/(100-Loss%) * S.P.

10. If an article is sold at a gain of say, 35%, then S.P. = 135% of C.P.

11. If an article is sold at a loss of say, 35%, then S.P. = 65% of C.P.

VOLUME AND SURFACE AREA -> IMPORTANT FACTS AND FORMULAE:I.

CUBIODLet length = l, breadth = b and height = h units. Then,

1. Volume = (l x b x h) cubic units.

2. Surface area = 2 (lb + bh + lh)II.

CUBELet each edge of a cube be of length a. Then,

1. Volume = a³ cubic units.

2. Surface area = 6a² sq. units.

3. Diagonal = v3 a units.III.

CYLINDERLet radius of base = r and Height (or length) = h Then,

1. Volume = (πr²h) cubic units.

2. Curved surface area = (2 π rh) sq. units.

3. Total surface area = (2πr h + 2πr² sq. units)

= 2πr (h + r) sq. units.IV.

CONELet radius of base = r and Height = h. Then,

1. Slant height, l = vh² + r ² units.

2. Volume = [1/3πr²h] cubic units.

3. Total surface area = (πrl + πr²) sq.units.V.

SPHERELet the radius of the sphere be r. Then,

1. Volume = [4/3πr3] cubic units.

2. Surface area = (4πr²) sq. units.VI.

HEMISPHERELet the radius of a hemisphere be r. Then,

1. Volume = [2/3 πr3] cubic units.

2. Curved surface area = (3πr²) sq. units.

3. Total surface area = (3πr²) sq. units.

Remember : 1 litre = 1000 cm³.

CLOCKS -> IMPORTANT FORMULAE :The face or dial of a watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.

A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.I. In 60 minutes, the minute hand gains 55 minutes on the hour hand.

II. In every hour, both the hands coincide once.

III. The hands are in the same straight line when they are coincident or opposite to each other.

IV. When the two hands are at right angles, they are 15 minute spaces apart.

V. When the hands are in opposite directions, they are are 30 minute spaces apart.

VI. Angle traced by hour hand in 12 hrs = 360°.

VII. Angle traced by munute hand in 60 min. = 360°.

PROBLEMS ON TRAINS -> IMPORTANT FORMULAE :1. a km/hr = [a * 5/18]m/s.

2. a m/s = [a * 18/5] km/hr.

3. Time taken by a trian of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres.

4. Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l + b) metres.

5. Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u>v, then their relatives speed = (u – v) m/s.

6. Suppose two trains or two bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v)m/s

7. If two trains of length a metres and b metres are moving in opposite directions at u

8. If two trains of length a metres and b metres are moving in the same direciton at u m/s and v m/s, then the time taken by the faster train to cross the

SURDS AND INDICES -> IMPORTANT FACTS AND FORMULAE :

1.LAWS OF INDICES :

(i) am * an = am + n(ii) am / an = am – n

(iii) (am)n = amn

(iv) (ab)n = anbn

(v) (a/b)n = an/ bn

(vi) a

^{0}= 12.

SURDS:Let a be rational number and n be a positive integer such that

a(1/n) = nva

3. LAWS OF SURDS :

(i) nva = a (1/n)

(ii) nvab = nva x nvb

(iii) nva/b = nva / nvb

(iv) (nva)n = a

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