Math Tricks....

(1).Speed Time and Distance shortcut tricks:----

Speed Time and Distance
This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam. Under below given some formula and more example for your better practice.

Anything we learn in our school days was basics and that is well enough for passing our school exams. Now the time has come to learn for our competitive exams. For this we need our basics but also we have to learn something new. That’s where shortcut tricks are comes into action.

Formula:
Distance = Speed x Time
Generally use this formula we can find the distance of any running train, car etc. If Speed of train or car is given with time and using this multiplying this two we can find the distance covered by train. The unit of distance is kilometers, meters, miles, etc.

Speed = Distance / Time
To find the speed we can divide Distances by Time.

The unit of Speed has written in fractions that is Km/hr ( written as Distance unit in numerator and Time units in the denominator ), Suppose 35 Km/hr.

Time = Distance / Speed
To find the Time we can divide distance by speed.

If in the question is Time unit given in minute then convert it into hours divide 60 before you use the equation to find the distance in miles.

and if say to find in minutes take to cover distance in meter and speed in Km / hr then Km / hr convert into m / sec, multiplied by 5 / 18.

B km / hr convert to m / sec = ( B x 5 / 18) m / sec.

B m / sec convert to km / sec =(B x 18 / 5 ) km / sec.

If the speeds ratio of P and Q is p : q, then to cover the same distances the ratio of the times taken by them is 1 / p : 1 / q, or q : p.

Suppose a man covers a certain distance at x km / hr and an equal distance at y km / hr. Then, average speed during the whole journey is ( 2 x y / x + y ) km / hr.

SPEED
Example 1: A bus covers a distance in 18 hours at the speed of 60 kms/hr. What would be the average speed of a bike which covers a distance of 270 kms. more than the bus in the same time ?

Answer : Distance = 60 x 18 = 1080 km.

Speed = 1080 + 270 / 18 = 75 km/hr.

Example 2: Suresh travel on car and covers a 360 km distances in 8 hours and Ramesh travel on car and covers a 405 km distances in 9 hours. What would be the sum of there speed of both cars ?

Answer: Speed of Suresh car = 360 / 8 = 45 km/hr,

Speed of Ramesh car = 405 / 9 = 45 km/hr

So, sum of both cars speed = ( 45 + 45 ) = 90 km/hrs.

Example 3:

Amir by car passes a 1200 m long road in 4 minutes. What would be his speed in Km/hr ?

Answer : Speed = ( 1200 / 4 x 60 ) m / sec = 5m / sec.

Convert it into Km /hr = 5 x 18 / 5 = 18km / hr.

Example 4:

A fast train covers a distance in 40 min, if it runs at a speed of 45kmph on an average. The speed at which the train must run to reduce the time of journey to 30min will be ?

Answer:

Time = 40 / 60 = 2 / 3.

given speed = 45kmph

Distance = Speed x Time.

Distance = 45 x 2 / 3 = 30km

Time =30 / 60 = 1 / 2hr

Speed = Distance / Time.

So, the new speed is = 30 x 2 = 60kmph.

Example 5:

Harish on tour travels first 160 km at 64 km /hr and the next 160 km at 80 km /hr. The average speed of for the first 320 km of the tour is:

Answer :

Total time taken by Harish is : = ( 160 / 64 + 160 / 8 ) hrs = 9 / 2 hrs.

So that Average speed = ( 320 x 2 / 9 ) km / hr = 71.11 km / hr.

Example 6:

A bike covers a distance of 450 m in 2 min 30 sec. What is the speed in Km / hr of the bike ?

Answer :

Step 1: Speed = ( 450 / 150 ) m / sec = 3 m / sec.

Step 2: now convert it into km / hr = 3 x 18 / 5 = 10.8 Km / hr.

So the speed of in Km / hr of the bike is 10.8 Km / hr.

Example 7:

A Car covers a certain distance in 7 hours at the speed of 73 Kms/hr. What should be the average speed of bus? Which travels a distance of 55 Kms, less than the car in the same time ?

Answer :

Step 1 : The distance covered by the bus = ( 73 x 7 ) = 511

Step 2 : The distance cover bus = 511 – 55 = 456 Km. So average speed of the bus = 456 / 7 = 65.14 Km/hr.

Example 8:

The ratio between two super fast trains is 6 : 8. if the second train runs 600 Kms in 6 hours, then what would be the speed of the first train ?

Answer :

Step 1: Let the speed of two trains be 6x and 8x Km /hr.

Then, then we find the value of x,

8x = 600 / 6 = 100

x = 100 / 8 = 12.5.

here is value of x is 12.5 we put in first train.

Step 2: Speed of first would be = ( 6 x 12.5 ) Km / hr = 75 Km / hr.
So the Speed of First train is 75 Km / hr.

Example 9:

A boy without any stoppage running on a road at an average speed of 80 km /hr, and with stoppage he covers the same distance at an average speed of 60 km / hr. How many minutes per hour does boy stop ?

Answer :

Let the total distance cover by boy on road is x km .

Time take to complete at a speed of 80 km / hours = x / 80 hours .

Time take to complete at a speed of 80 km / hours = x / 60 hours .

So he stop to rest ( x / 80 – x / 60 ) hours = 20x / 60 x 80 = x / 240 hours .

So he rest per hour = x / 240 / x / 60 = x / 240 x 60 / x = 1 / 4 hours = 15 minutes .

Shortcut Tricks :

Time of rest per hour = ( Difference of speed / Speed without stoppage )
( 80 – 60 ) / 80 = 1 / 4 = 15 minutes.

Example 10:

A man walking at the rate of 4kmph to cover certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in what time ?

Answer:

we know the formula of
Distance = speed x Time

So, Time given = 2 hr 45 min = 2×60 min+45 min=165 min than 165 min / 60 min = 11 / 4 hr

Distance = 4 x 11 / 4 = 11 km

So, Time required to cover distance in speed of 16.5 kmph

Time = D / S = 11 / 16.5 = 40 min.

Example 11:

A train cover a distance of 16 km in 10 minutes. If its speed is decreased by 6 km/hr the time taken by it to cover the same distance will be :

Answer : Speed = (16 x 60 / 10) = 96 km/hr.

After decreased speed new speed is = (96-6) = 90km / hr.

So, Time taken by 16 x 60 / 90 = 32 / 3 min.

Example 12:

Rita can travel a journey in 10 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the the total journey.

Answer : Let her total distance be x km.

x/2/21 + x/2/24 = 10

15x = 168 x 20

x = (168 x 20/15) = 224 km.

Example 13:

The average speed of a car is 6 / 4 the average speed of a bike. If the bike passes 304 kms in 19 hours, Find how much distance would be covered by car in 12 hours ?

Answer: bike speed = 304 / 19 = 16 km/hr.

Avg speed of car = bike x 6 / 4 = 16 x 6 / 4 = 24 km/hr.

Distance = 24 x 12 = 288 kms.

Example 14:

A girl goes to his college from his house at a speed of 3 Km / hr and return at speed of 2 km /hr. If he takes 5 hours in going and coming, the distance between his house and college is:

Answer :

Average speed = ( 2 x 3 x 2 / 2 + 3 ) km / hr = 12 / 5 km / hr.

Distance between his house and college he travailed in 5 hours: ( 12 / 5 x 5 ) km = 12 km.

The distance between his house and college is : ( 12 / 2 ) = 6 km.

Example 15:

A train traveling at 90 kmph overtakes a bike traveling at 54 kmph in 30 seconds. What is the length of the train in meters ?

Answer:

The distance travailed by the train overtaking the bike is the same as the length of the train.

both the object move in same direction .

so, ( 90 – 54 ) = 36kmph

convert kmph to m/sec = 36 x 5 / 18 = 10 m / sec.

Time taken in 40 sec.

distance travailed = 10 x 30 = 300 meters.

Example 16: The fast train covers 325 kms in 5 hours and the average speed of car is 20% more than the average speed of the train. So the bike in 6 hours what distance should covers.

Answer : Speed = distance / time = 325 / 5 = 65 km/hr.

average speed of car is 20% more = 65 x 120 / 100 = 78 km/hr.

Distance covers in 6 hours is 78 x 6 = 468 kms.

Example 17:

A Honda car does complete a journey in 12 hours, The first half hours complete at 23 km / hr and the second half at 25 km / hr. What would be the distance ?

Answer :

let the distance be x km.

the car has time taken to complete the x / 2 km at a speed of 23 km / hr.

the car has time taken to complete the x / 2 km at a speed of 25 km / hr.

So , total time taken to complete the whole journey is,

= x / 2 x 23 + x / 2 x 25 = 12 hrs

x = 2 x 12 x 23 x 25 / ( 23 + 25 )

x =287.5

Short cut tricks: Distance = 2 x Time x speed 1 x speed 2 / s1 + s2

Here s1 = speed during first half and s2 = Speed of second half of journey

Distance = 2 x 12 x 23 x 25 / ( 23 + 25 ) = 287.5 km.

Example 18:

With a uniform speed a bike covers the distance in 10 hours. When speed of bike is increased by 4 km / hr, the same distance could have been covered in 8 hours. What would be the distance covered by bike ?

Answer :

let the distance be x km . Then ,

x / 8 – x / 10 = 4

x = 160 km.

Example 19:

A civic car covers 258 Kms, in 3 hours. The average speed of a bike is 45% more than the average speed of the car. How much distance will the bike cover in 6 hours ?

Answer :

Step 1: Speed = 258 / 3 = 86.

Step 2: 86 x 145 / 100 = 124.7 Distance = 124.7 x 6 = 748.2 Km.

Example 20: Rajib walks 170 meters every day. How many kilometers will he made in 4 week ?

Answer :170 x 28 = 4760 meter

Convert meter to km 4760 / 1000 = 4.760 kms.

Example 21:

A bus covers the intial first 46 Kms in 42 minutes and remaining 26 kms covers in 38 minutes, Find the average speed of the car.

Answer :

46 + 26 = 72 (add both distances)

72 x 60 / 80 = 54 km/hr.

Example 22:

Ajay Passes a car in 16 seconds, The same car passes a lamp post in 6 seconds,
Find respective ratio between speed of car and speed of the man.

Answer: 1 / 16 : 1 / 6 = 3 : 8

So, the respective ratio between speed of car and speed of the man is 3 : 8.

Example 23:

A fast train covers a distance in 40 min, if it runs at a speed of 45 kmph on an average. The speed at which the train must run to reduce the time of journey to 30 min will be ?

Answer:

Time = 40 / 60 = 2 / 3.

given speed = 45 kmph

Distance = Speed x Time.

Distance = 45 x 2 / 3 = 30 km

Time =30 / 60 = 1 / 2 hr

Speed = Distance / Time.

So, the new speed is = 30 x 2 = 60 kmph.

Example 24:

A man walking at the rate of 4 kmph to cover certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in what time ?

Answer:

we know the formula of

Distance = speed x Time

So, Time given = 2 hr 45 min = 2×60 min+45 min=165 min than 165 min / 60 min = 11 / 4 hr

Distance = 4 x 11 / 4 = 11 km

So, Time required to cover distance in speed of 16.5 kmph

Time = D / S = 11 / 16.5 = 40 min.

Example 25:

A train traveling at 90 kmph overtakes a bike traveling at 54 kmph in 30 seconds. What is the length of the train in meters ?

Answer:

The distance travailed by the train overtaking the bike is the same as the length of the train.

both the object move in same direction .

so, ( 90 – 54 ) = 36 kmph

convert kmph to m/sec = 36 x 5 / 18 = 10 m / sec.

Time taken in 40 sec.

distance travailed = 10 x 30 = 300 meters.

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(2). Glossary Tips & Tricks
Natural Numbers: 1, 2, 3, 4…..
Whole Numbers: 0, 1, 2, 3, 4…..
Integers: ….-2, -1, 0, 1, 2 …..

Rational Numbers: Any number which can be expressed as a ratio of two integers for example a p/q format where ‘p’ and ‘q’ are integers. Proper fraction will have (p<q) and improper fraction will have (p>q)

Factors: A positive integer ‘f’ is said to be a factor of a given positive integer 'n' if f divides n without leaving a remainder. e.g. 1, 2, 3, 4, 6 and 12 are the factors of 12.

Prime Numbers: A prime number is a positive number which has no factors besides itself and unity.

Composite Numbers: A composite number is a number which has other factors besides itself and unity.

Factorial: For a natural number 'n', its factorial is defined as: n! = 1 x 2 x 3 x 4 x .... x n (Note: 0! = 1)

Absolute value: Absolute value of x (written as |x|) is the distance of 'x' from 0 on the number line. |x| is always positive. |x| = x for x > 0 OR -x for x < 0

Funda: The product of ‘n’ consecutive natural numbers is always divisible by n!

Funda: Square of any natural number can be written in the form of 3n or 3n+1. Also, square of any natural number can be written in the form of 4n or 4n+1.

Funda: Square of a natural number can only end in 0, 1, 4, 5, 6 or 9. Second last digit of a square of a natural number is always even except when last digit is 6. If the last digit is 5, second last digit has to be 2.

Funda: Any prime number greater than 3 can be written as 6k ±1.

Funda: Any two digit number ‘pq’ can effectively be written as 10p+q and a three digit number ‘pqr’ can effectively be written as 100p+10q+r.

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(3).HCF and LCM Tips & Tricks
For two numbers, HCF x LCM = product of the two.

HCF of Fractions = HCF of numerator/LCM of Denominator

LCM of Fractions = LCM of numerator/HCF of denominator

Relatively Prime or Co-Prime Numbers: Two positive integers are said to be relatively prime to each other if their highest common factor is 1.
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(4). Laws of Indices Tips & Tricks

Funda: If am = an, then m = n

Funda: If am = bm and m ≠ 0;

Then a = b if m is Odd
Or a = ± b if m is Even

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(5).Profit and Loss Tips & Tricks
%Profit / Loss =

In case false weights are used while selling,

% Profit =

Discount % = (Marked Price - Selling Price / Marked Price)100

Funda: Effective Discount after successive discount of a% and b% is Effective Discount when you buy x goods and get y goods free is (y/x+y)100

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(6). Percentages Tips & Tricks
Fractions and their percentage equivalents:

Funda: r% change can be nullified by change in another direction. Eg: An increase of 25% in prices can be nullified by a reduction of [100*25/(100+25)] = 20% reduction in consumption.

Funda: If a number ‘x’ is successively changed by a%, b%, c%...

=> Final value =

Funda: The net change after two successive changes of a% and b% is

Note :- If you want any other formula, any content related to it, then reply me... It's my pleasure