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RATIO AND PROPORTION
The comparison of two quantities by the process of division method is called as ‘Ratio’ between two numbers. When two ratios are equal in value, then they are said to be in proportion.
Ratio and percentage can be used interchangeably.
Infact, there come many instances where solving a question becomes easier using ratio even if percentage is given in the question and vice versa.
‘In a school, there are 200 students. 40% of them are boys. How many more boys should be added to the school such that the ratio of boys to girls in the school becomes 1:1?’
40% percent means 2/5, which means ratio of boys to girls initially is 2:3.
The new ratio has to be 1:1 or we may write it as 3:3(as the no. of girls remain unchanged).
Since 5(2+3) means 200, hence 6(3+3) means 240.
Therefore, 40 more boys are added.
‘The sum of four numbers is 253. The ratio of the first to the second is 2 : 3. The ratio of the second to the third is 5 : 6. The ratio of the third to the fourth is 8 : 9. What is the average of the second and the third number?’
Here, we need to make the given four numbers proportionate to one another.
Suppose four numbers are A,B,C and D respectively.
A:B:C=10:15:18 and C:D=8:9.
Hence, A:B:C:D= 80:120:144:162.
Sum of all these is= 506
506 is two times 253.
Hence , four numbers are 40,60,72 and 81.
‘A family consists of father, mother, son and daughter. Ratio of the weight of the father to the weight of the son is 3 : 2. Ratio of the weight of the son to the weight of the mother is 5 : 6. If the weight of the daughter is 35 kg, half the weight of the father, find the weight of the mother.’
Ratio of weights of father, son and mother= 15:10:12.
Suppose weight of the father is 15x kg.
According to question, weight of the father is equal to 35×2=70 kgs.
Weight of mother=70/15×12= 56 kgs