APTITUDE FORMULA
TIME AND DISTANCE -> IMPORTANT FACTS AND FORMULA
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.
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PROFIT AND LOSS ->
IMPORTANT FACTS AND FORMULA
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.Pis 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.
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VOLUME AND
SURFACE AREA -> IMPORTANT FACTS AND FORMULA
I. CUBOID
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)
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 = √h² + r ² 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 =
[4/3 Πr3] cubic units.
2. Surface
area = (4Πr²) sq. units.
VI. HEMISPHERE
Let 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 liter = 1000 cm³.
BANKERS DISCOUNT ->
IMPORTANT CONCEPTS
Bankers’ Discount : Suppose a
merchant A buys goods worth, say Rs. 10,000 from another merchant B at a
credit of say 5 months. Then, B prepares a bill, called the bill of exchange. A
signs this bill and allows B to withdraw the amount from his bank account after
exactly 5 months.
The date exactly after 5 months
is called nominally due date. Three days (known as grace days) are added to it
to get a date, known as legally due date.
Suppose B wants to have the
money before the legally due date. Then he can have the money from the banker
or a broker, who deducts S.I. on the face value (i.e., Rs. 10,000 in this case)
for the period from the date on which the bill was discounted (i.e., paid by
the banker) and the legally due date. This amount is known as Banker’s Discount
(B.D.)
Thus, B.D. is the S.I. on the
face value for the period from the date on which the bill was discounted and
the legally due date.
Banker’s Gain (B.G.) = (B.D.) -
(T.D.) for the unexpired time.
Note : When the date of the
bill is not given, grace days are not to be added.
BANKERS DISCOUNT -> IMPORTANT FORMULA
I. B.D. = S.I. on bill for
unexpired time.
II. B.G. = (B.D.) - (T.D.) =
S.I. on T.D. = (T.D.)² / R.W.
III. T.D. = √P.W. * B.G.
IV. B.D. = [Amount * Rate *
Time / 100]
V. T.D. = [Amount * Rate * Time / 100 + (Rate * Time)]
VI. Amount = [B.D. * T.D. /
B.D. - T.D.]
VII. T.D. = [B.G. * 100 / Rate
* Time]
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CLOCKS -> IMPORTANT FORMULA
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 minute
hand in 60 min. = 360°.
Too Fast and Too Slow : If a
watch or a clock indicates 8.15, when the correct time is 8, it is said to be
15 minutes too fast.
On the other hand, if it
indicates 7.45, when the correct time is 8, it is said to be 15 minutes too
slow.
TRUE DISCOUNT ->
IMPORTANT CONCEPTS
Suppose a man has to pay Rs.
156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100
at 14% will amount to Rs. 156 in 4 years. So, the payment of Rs. 100 now will
clear off the debt of Rs. 156 due 4 years hence. We say that :
Sum due = Rs. 156 due 4 years hence;
Present worth (P.W.) = Rs.100;
True Discount (T.D.) = Rs. (156
- 100) = Rs. 56 = (Sum due) - (P.W.).
We define : T.D. = Interest on
P.W.
Amount = (P.W.) + (T.D.).
Interest is reckoned on P.W.
and true discount is reckoned on the amount.
TRUE DISCOUNT ->
IMPORTANT FORMULA
Let rate = R% per annum and
Time = T years. Then,
I. P.W. = 100 * Amount / 100 +
(R*T) = 100 * T.D. / R * T
II. T.D. = (P.W.)* R * T / 100
= Amount * R * T / 100 + (R * T)
III. Sum = (S.I.) * (T.D.) /
(S.I.) - (T.D.)
IV. (S.I.) - (T.D.) = S.I on
T.D.
V. When the sum is put at
compound interest, then P.W. = Amount / [1+R/100]T;
PROBLEMS ON TRAINS ->
IMPORTANT FORMULA
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 meters to pass a pole or a standing man or a signal post is equal to
the time taken by the train to cover l meters.
4. Time taken by a train of
length l meters to pass a stationary object of length b meters is the time
taken by the train to cover (l + b) meters.
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 meters and b meters are moving in opposite directions at u
8. If two trains of length a meters and b meters are moving
in the same direction at u m/s and v m/s, then the time taken by the faster
train to cross the
