Site Links

Pages

Wednesday, July 15, 2015

Simple and Shortcut Trick & Concept to Solve Ratio and Proportion


                                         Ratio & Proportion

Ratio is comparison between two quantities of the same kind of unit is the ratio of one quantity to another. Two quantities of different kinds cannot be compared. Thus there is no relation between 20 rupees and 20 men.

The ratio of a and b is usually written as a : b   or     a / b.

We see a lots of ratios in daily life, whenever we required he two number then we uses the ratios. We can also find out how many times a number is greater than others.

We can compare the salary of two friends, suppose A salary is 20 and B salary is 10
So the ratio is 20 : 10 = 2: 1 or  2 / 1    .

Comparing / Ranking Ratios.
We will see the simple technique, we will not look for LCM and other technique. We can rank or Compare the ratios.



Example we have to rank the ratios  2/3, 5/6, 13/14 , 7/8   we have to rank them, which one is highest, then look for the lowest. For that we will arrange them in Descending order.(which mean the Highest First.)  2/3 , 5/6 , 13/14, 7/8 for ranking we will see the Difference between the Numerator and Denominator.

In the First case the Difference is 1st, 2nd , 3rd and 4th cases also the Difference is 1 that mean Same in all cases. Whenever the difference is same just need to see the numerators and compare the numerators. In this case 13 is the highest no so 13/14  Will be the largest fraction, followed by 7, then 5 and then  2.
So we will rank the Fractions. (1st) 13/14 , (2nd)7/8 , (3rd) 5/6 , (4th) 2/3

We did that, we saw Numerator, then we saw Denominator, then we found the Differences.
We saw that the difference is same, so we went on to see the greater the numerator and greater will be the fractions.

Continue Ratio :  for the continue ratio we need to understand few basic things. For that we will take an example.
Example 1: There was a farmer who had wealth of 12000, he have cash with him and he want to give it to his two son A & B in the 1 : 2 ratio, so how do they actually get it.
Solution : Total amount is 12000
We have to divide it in 1 : 2 ratio, first add the ration 1 + 2 = 3
So  A  will get  1/3  share & B will get  2/3 share.
A share = 1/3*12000 = 4000
B share = 2/3*12000 = 2*4000 = 8000

 Example 2 : There is 60, 000 is in the ration of A:B = 1 : 2 and B : C = 2 : 3 its not in continue ratio.
Solution :  
So we will focus on B and make it equal. B is Same here.
For that   write ratio in form    A :  B              =        1 : 2                                                               and                                              B : C         =            2 : 3      
          
Multiply A by B,  and  B multiply by  B itself and B  multiply by C also  = A×B : B×B : B×C
                              =  1× 2 : 2×2 :  2×3  =  2 : 4 : 6    =  minimize the ratio =  1 : 2 : 3   = 6

So  A =1/6 × 60,000 = 10,000
      B = 2/6× 60,000  = 20,000
      C =3/6 × 60,000  = 30,000

0 comments: