**Ratio and Proportion Aptitude Shortcuts Pdf :**

In this section, we will learn the shortcuts which are much helpful to solve ratio and proportion problems.

If you would like to have the shortcuts on ratio and proportion as pdf document,

**Shortcut 1 : **

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

**Shortcut 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.

**Shortcut 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

**Shortcut 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.

**Shortcut 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

**Shortcut 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

**Shortcut 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.

**Shortcut 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

**Shortcut 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.

**Shortcut 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.

**Shortcut 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.

**Shortcut 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.

**Shortcut 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.

**Shortcut 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.

If you would like to have the above shortcuts on ratio and proportion as pdf document,

After having gone through the stuff given above, we hope that the students would have understood the shortcuts on ratio and Proportion.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

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

**OTHER TOPICS **

**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 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**