1.TIME AND DISTANCE ->IMPORTANT FACTS ANDFORMULAE
1. Speed = [Distance/Time],
Time = [Distance/Speed],
Distance = (Speed*Time)
2. x km/hr = [x*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 is
1/a : 1/b or b:a.
4. x m/sec = [x*18/5] km/hr.
5. 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 journey is [2xy/x+y] km/hr.
2.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 sold, is called its
Selling Price, abbreviated as S.P.
Profit or Gain: If S.P. is greater than C.P., the seller is said to
have a Profit or Gain.
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.
3.VOLUME AND SURFACE AREA ->
IMPORTANT FACTS
AND FORMULAE
I. CUBIOD
Let 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)
3. Diagonal = ( + + ℎ)
II. CUBE
Let each edge of a cube be of length a. Then,
1. Volume = a³ cubic units.
2. Surface area = 6a² sq. units.
3. Diagonal = √3 a units.
III. CYLINDER
Let radius of base = r and Height (or length) = h Then,
1. Volume = (Πr²h) cubic units.
2. Curved surface area = (2Πrh) sq. units.
3. Total surface area = (2Πrh + 2Πr² sq. units)
= 2Πr (h + r) sq. units.
IV. CONE
Let radius of base = r and Height = h. Then,
1. Slant height, l = ( + ℎ) units.
2. Volume = [1/3 Πr²h] cubic units.
3. Total surface area = (Πrl + Πr²) sq. units.
V. SPHERE
Let the radius of the sphere be r. Then,
1. Volume = [4Πr3/3] cubic units.
2. Surface area = (4Πr²) sq. units.
VI. HEMISPHERE
Let the radius of a hemisphere be r. Then,
1. Volume = [2Πr3/3] cubic units.
2. Curved surface area = (2Πr²) sq. units.
3. Total surface area = (3Πr²) sq. units.
Remember: 1 litre = 1000 cm³.
4.BOATS AND STREAMS ->
IMPORTANT FACTS AND
FORMULAE
I. In water, the direction along the stream is called
downstream.
And, the direction against the stream is called upstream.
II. If the speed of a boat in still water is u km/hr and the
speed of the stream is v km/hr, then:
Speed downstream = (u + v) km/hr
Speed upstream = (u - v) km/hr.
III. If the speed downstream is a km/hr and the speed
upstream is b km/hr, then:
Speed in still water = 1/2 (a + b) km/hr
Rate of stream = 1/2 (a - b) km/hr
5.PARTNERSHIP ->
IMPORTANT FACTS AND FORMULAE
I. Partnership: When two or more than two persons run a
business jointly, they are called partners and the deal is
known as partnership.
II. Ratio of Division of Gains:
(i) When investments of all the partners are for the same
time, the gain or loss is distributed among the partners in
the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a
year in a business, then at the end of the year:
(A’s share of profit): (B’s share of profit) = x:y.
(ii) When investments are for different time periods, then
equivalent capitals are calculated for a unit of time by
taking (capital * number of units of time). Now, gain or loss
is divided in the ratio of these capitals.
Suppose A invests Rs. x for p months and B invests Rs. y for
q months, then (A’s share of profit) : (B’s share of profit) =
xp : yq.
III. Working and Sleeping Partners: A partner who manages
the business is known as working partner and the one who
simply invests the money is a sleeping partner.
6.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 train 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
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