RATIO AND PROPORTION APTITUDE SHORTCUTS PDF

About "Ratio and Proportion Aptitude Shortcuts Pdf"

Ratio and Proportion Aptitude Shortcuts Pdf :

In this section, we are going to see the shortcuts which would be much helpful to solve ratio and proportion problems.

Ratio and Proportion Shortcuts

Hint 1 :

a/b is the ratio of a to b . That is a : b. 

Hint 2 :

When two ratios are equal, they are said to be in proportion.

Example :

If a : b  =  c : d, then a, b, c and d are proportion.

Hint 3 :

Cross  product rule in proportion :

Product of extremes  =  Product of means

Example :

Let us consider the proportion a : b  =  c : d

Extremes  =  a, d

Means  =  b, c

By cross product rule, we have

ad  =  bc

Hint 4 :

Inverse ratios :

b:a is the inverse ratio of a:b and vice versa.

That is, a : b and b : a are the two ratios inverse to each other.

Hint 5 :

Verification of inverse ratios :

If two ratios are inverse to each other, then their product must be 1.

That is, a:b & b:a are two ratios inverse to each other.

Then, (a : b)  (b : a)  =  (a/b) ⋅ (b/a)  =  ab/ab  =  1

Hint 6 :

If the ratio of two quantities is given and we want to get the original quantities, we have to multiply both the terms of the ratio by some constant, say “x”.

Example :

The ratio of earnings of two persons is 3 : 4.

Then,

the earning of the first person  =  3x

the earning of the second person  =  4x

Hint 7 : 

If we want compare any two ratios, first we have to express the given ratios as fractions.

Then, we have to make them to be like fractions.

That is, we have to convert the fractions to have same denominators.

Example :

Compare: 3 : 5 and 4 : 7.

First, let us write the ratios 3 : 5 and 4 : 7 as fractions.

That is 3/5 and 4/7.

The above two fractions do not have the same denominators. Let us make them to be same.

For that, we have to find L.C.M of the denominators (5,7).

That is, 5 ⋅ 7  =  35.

We have to make each denominator as 35.

Then the fractions will be 21/35 and 20/35.

Now compare the numerators 21 and 20.

21 is greater

So the first fraction is greater.

Hence the first ratio 3 : 5 is greater than 4 : 7.

Hint 8 :

If two ratios P : Q and Q : R are given and we want to find the ratio P : Q : R, we have to do the following steps.

First find the common tern in the given two ratios P : Q and Q : R. That is Q.

In both the ratios try to get the same value for “Q”.

After having done the above step, take the values corresponding to P, Q, R in the above ratios and form the ratio P : Q : R.  

Example :

If P : Q  =  2 : 3 and Q : R  =  4 : 7, find the ratio P : Q : R.

In the above two ratios, we find “Q” in common.

The value corresponding to Q in the first ratio is 3 and in the second ratio is 4.

L.C.M of (3, 4)  =  12.

So, if multiply the first ratio by 4 and second by 3,

we get P : Q  =  8 : 12 and Q : R  =  12 : 21

Now we have same value (12) for “Q” in both the ratios.

Now the values corresponding to P, Q & R are 8, 12 & 21.

Hence the ratio P : Q : R  =  8 : 12 : 21

Hint 9 :

If the ratio of speeds of two vehicles in the ratio a : b, then time taken ratio of the two vehicles would be b : a.

Example :

The ratio of speeds of two vehicles is 2 : 3. Then time taken ratio of the two vehicles to cover the same distance would be 3 : 2. 

Hint 10 :

If the ratio of speeds of two vehicles in the ratio a : b, then the distance covered ratio in the same amount of time  would also be a : b.

Example :

The ratio of speeds of two vehicles is 2 : 3. Each vehicle is given one hour time. Then, the distance covered by the two vehicles would be in the ratio 2 : 3.  

Hint 11 :

If A is twice as good as B, then the work completed ratio of A and B in the same amount of time would be 2 : 1.

Example :

A is twice as good as B and each given 1 hour time.  If A completes 2 unit of work in 1 hour, then B will complete 1 unit of work in one hour.

Hint 12 :

If A is twice as good as B, then the tame taken ratio of A and B to do the same work would be 1 : 2.

Example :

A is twice as good as B and each given the same amount of work to complete. If A takes 1 hour to complete the work, then B will take 2 hours to complete the same work.

Hint 13 :

If “m” kg of one kind costing $a per kg is mixed with “n” kg of another kind costing $b per kg, then the price of the mixture would be $ (ma+nb) / (m+n) per kg.

Hint 14 :

If one quantity increased or decreases in the ratio a : b,

then the new quantity is  =  “b” of the original quantity / a

More clearly, new quantity  =  (“b”  original quantity) / a

Example :

David weighs 56 kg. If he reduces his weight in the ratio 7 : 6, find his new weight.

New weight  =  (6  56) / 7  =  48 kg.

Hence, David’s new weight is 48 kg.  

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ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

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Simplifying radical expression

Comparing surds

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Negative exponents rules

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Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

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Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

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Special line segments in triangles worksheet

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Properties of triangle worksheet

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Quadratic equations word problems worksheet

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Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

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Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

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Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

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Domain and range of trigonometric functions 

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Geometry dictionary

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Angle bisector theorem

Basic proportionality theorem

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Ratio and proportion word problems

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Word problems on sets and venn diagrams

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Percent of a number word problems

Word problems on constant speed

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Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6