7th Class Mathematics Comparing Quantities Ratio

     Introduction

In this chapter we will study about the comparison of two or more quantities. When we compare only two quantities of same kind, it is called ratio and more than two quantities is called proportion.  

     Ratio

A ratio is a relation between two quantities of same kind. Comparison is made between the two quantities by considering what part of one quantity is that of the other quantity. The two quantities are called the terms of ratio. If \[x\]and y are two quantities of same kind then the ratio of \[x\] to \[y\]is \[x/y\]or \[x:y.\]It is represented by \[x:y.\]  

      Important Points Related to Ratio

• The first term of ratio is called antecedent and the second term is called the consequent.
• If \[\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=..............\]then each ratio is equal to \[\frac{a+c+e............}{b+d+f............}\]
• Multiplication and division by the same number (except zero) with antecedent and consequent of the ratios are equal in values, the resultant ratio remains unchanged.  

Jennifer mixes 600 ml of orange juice with 2L of apple juice to make a fruit drink. Find the ratio of orange juice to apple juice in its simplest from.

(a) 1:3                                                  

(b) 300:1

(b) 3:10                                                

(d) 3:2

(e) None of these  

Answer: (c)

Explanation

\[600:2000=\frac{600}{2000}=\times \frac{6\times 100}{20\times 100}=\frac{6}{20}=\frac{3\times 2}{2\times 10}=\frac{3}{10}=3:10\]  

If \[4x+3y:6x+5y=\frac{11}{17}\]then find\[~x:y.\]

(a) 0:1                                                  

(b) 2:1

(b) 1:0                                                  

(d) 5:0

(e) None of these                  

Answer: (b)

Explanation                

\[\frac{4x+3y}{6x+5y}=\frac{11}{17}\Rightarrow 17(4x+3y)=11(6x+5y)\]            

\[\Rightarrow 68x+51y=66x+55y\Rightarrow 68x-66x\text{ }=55y-51y\]

\[\Rightarrow 2x=4y\Rightarrow \frac{x}{y}=\frac{4}{2}\Rightarrow x:y=2:1\]    

  If A, B, C, D are quantities of same kind and the ratio of A to B is 3 : 4, B to C is 5 : 7 and C to D is 8 : 9 then the ratio of

1. A to C is 15 : 28

2. B to D is 40 : 63

3. A to D is 10 : 21  

Which one of the following options is correct?  

(a) 1, 2 and 3                                     

(b) 1 and 2          

(b) 2 and 3                                          

(d) 1 and 5

(e) None of These  

Answer: (a)  

Explanation                

\[\frac{A}{B}=\frac{3}{4},\frac{B}{C}=\frac{5}{7}\And \frac{C}{D}=\frac{8}{9}\Rightarrow A=\frac{3}{4}B=\frac{5}{7}C\Rightarrow A=\frac{3}{4}\times \frac{5}{7}C\] Or \[\frac{A}{C}=\frac{15}{28}\]                 \[\Rightarrow C=\frac{8}{9}D\Rightarrow B=\frac{5}{7}\times \frac{8}{9}D\Rightarrow B\frac{40}{63}D\]Or \[\frac{B}{D}=\frac{40}{63}\]                

\[\Rightarrow A=\frac{3}{4}B=\frac{3}{4}\times \frac{40}{63}D\frac{10}{21}D\Rightarrow \frac{A}{D}=\frac{10}{21}\]  

  Two numbers are in the ratio of 2 : 3. If sum of their squares is 468 then Find the numbers.

(a) (12, 16)                                         

(b) (12, 18)

(c) (14, 20)                                          

(d) (12, 22)

(e) None of these  

Answer: (b)  

Explanation

Let one number be \[2x\] and other number will be 3x then \[{{(2x)}^{2}}+{{(3x)}^{2}}=468\]                

\[\Rightarrow 4{{x}^{2}}+9{{x}^{2}}=468\Rightarrow 13{{x}^{2}}=468\Rightarrow x2=36\therefore x=6\]

Hence, first number be \[6\times 2=12\] and other number\[6\times 3=18\].  

A mixture contains milk and water in the ratio 5:3. If 4 liters of this mixture is replaced (from20 liter) by 4 liters of milk then the ratio of milk to water in new mixture will be:

(a) 7:3                                                  

(b) 8:3

(c) 9:7                                                   

(d) 4:6

(e) None of these

Answer: (a)