### Ratio and Proportion Maths problems with examples & solution

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__Ratio__ ,__Proportion__ And __Percentage__

**Ratio/proportion-**Ratio is a relation between two quantities i.e. one quantity is how many times of second quantity.

**e.g**. If salary of A is 100 and salary of B is 200 then ratio between the salary of two would be 1:2 or you can say salary of B is two times of salary of A.And in proportion we will write it as 1/2.

here, in fraction we consider base as always 100%. we take the base as 100% i.e. 2

so if 2=100% then 1 will be 50%

**Percentage-**Percentage is simply called number of parts per 100 of some unit. It is a way to express a number as a fraction of hundred.

**e.g.**If one student score 500 hundred marks our of 1000 then if we convert on the base of 100 it becomes 50 i.e. percentage will be 50%.**NOTE-**Actually both the terms are numerically different. but same in understanding.Lets discuss how?

In first example ratio b/w salary of two person is 1:2.

Now if I ask you what percentage of salary of A is B????

Then of course, it will be 1/2*100= 50%

Here we take the base as 100% i.e. 2

So if 2=100% then 1 will be 50%Now if I ask you what percentage of salary of A is B????

Then of course, it will be 1/2*100= 50%

Here we take the base as 100% i.e. 2

On the other hand , In 2nd example if I ask you what will be the ratio between the obtained marks and total marks??

Then of course, it will be 500/1000=1/2=1:2

Then of course, it will be 500/1000=1/2=1:2

So from here we can conclude that ratio and percentage complement each other and we can derive a relation between both. so, to convert a ratio in percentage we multiply by 100 and to convert a percentage into ratio we divide by 100.

**Now, we will make a table between ratio/proportion and percentage**

Ratio | %Age | Ratio | %Age |
---|---|---|---|

1/1 | 100% | 1/11 | 9.09% |

1/2 | 50% | 1/12 | 8.33% |

1/3 | 33.3% | 1/13 | 7.69% |

1/4 | 25% | 1/14 | 7.14% |

1/5 | 20% | 1/15 | 6.6% |

1/6 | 16.6% | 1/16 | 6.25% |

1/7 | 14.28% | 1/17 | 5.8% |

1/8 | 12.5% | 1/18 | 5.5% |

1/9 | 11.11% | 1/19 | 5.20% |

1/10 | 10% | 1/20 | 5% |

Then we know 1/9= 11.11%

11.11*2=2*1/9 which means 22.22% = 2/9.

By this method you can find the fraction of other percentage.

**Example 1-**find 42.84% of 210?**Case 1**-If you do not know the conversion b/w fraction and percentage,

then 42.84/100*210=????

By this way it will be very lengthy and you will fail to find exact value.

By this way it will be very lengthy and you will fail to find exact value.

**Case 2**-If you know the conversion,

We know, 14.28%=1/7

Which implies that 14.28*3%= 3*1/7

That makes 42.84%=3/7

Which implies that 14.28*3%= 3*1/7

That makes 42.84%=3/7

So 3/7*210=90

So here you can see if you know relation b/w two you can find it easily.

Practice as much as you can to be master of these problems. you can use these properties in every topic of Quant. so before moving ahead, become a master of it.

#### Simple tricks and formula to solve question by percentage and fraction

**1.**Successive Increase/Decrease

If a term is increased/decreased for 2 times then it is called successive increase/decrease.

**e.g**. If a term is increased by 20% and 30% then what will be net percentage increase??*As we know every value is 100% in itself , if 20% is increased for first then it will be 120% after the first increment .*

After 2nd increment of 30%, it will become 120*130/100=156%

so net increment will be 56%.

why we used 130/100? because after first increment value would be 120% which will be 100% in itself. so increment of 30% will make it 130% of 120.

####
**Alternative formula is( a+b+ab/100) % where we will use negative sign for decrease.**

**Example 2-**Salary of A,B,C is in the ratio of 2:3:4. total salary of three is 27000. what will be the salary of B?Sol. we know total salary is 27000.

By ratio we know there are 9 parts(2+3+4) of salary.

9 parts =27000

1 parts=3000

so,B has 3 parts so salary of B will be 9000.

**Example 3**-Salary of A,B,C is in the ratio of 2:3:4. if salary of B is 12000. find the salary of A and C.Sol. In 2nd example , total salary was given i.e. for 9 parts. here salary of B is given i.e. 12000 but in ratio B has only 3 Parts

so, 3 parts= 12000

1 parts =4000

therefore, salary of A(2 parts)= 2*4000=8000

Salary of C(4 parts)=4*4000=16000

so, we have got an idea that we can play with ratio according to question.

**Example 4**-The Income of Ram and Shyam is 8:11. and their expenditure are in the ratio of 7:10. if each of them saves 5000, what are their income and expenditure??Sol. Now we know , income = expenditure+saving

So each saves same amount so difference in their ratio must be same.

**Quicker approach**

So, saving is 1 parts, which is 5000

So Income of Ram and Shyam will be 40000( 5000*8) and 55000( 5000*11)

and expenditure of Ram and Shyam will be 35000(5000*7) and 50000(5000*10) respectively.

**Example 5**-age of Virender is 2 times more than that of age of Akshay. if their total age is 90. what will be their age respectively.Sol. as it is given that Virender is 2 times older than that of Akshay

so first convert it in ratio i.e. 2:1

total parts = 3 parts=90

1 parts =90/3=30

therefore age of virender and akshay will be 60 and 30 respectively.

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