Let’s jump into basics first

Basic Concepts

Ratio: It defines the relationship between two things which shows how many times a thing is corresponding to another thing. For example,1:2

Proportion: It defines two ratios are equal to each other. Each quantity such as A,B,C,D are known as terms.

A proportion can be divided into two categories, means, and extremes
So, the initial and last one is extremes and inbetween them are means.

Which implies, product of extremes are equivalent to product of means -> AD = BC

When a,b,c terms are related to one another ( having same unit ), then they are known as continuous proportion:

i.e  a : b :: b : c

Important Points to Remember

These are some of the properties of proportion:

• Invertendo -> a : b = c : d, then b : a = d : c
• Addendo -> a : b = c : d = e : f = …. , then (a + c + e +….) : b + d + f +…)
• Subtrahendo -> a : b = c : d = e : f = …. , then (a – c – e -….) : b – d – f -…)
• Dividendo -> a : b = c : d, then (a – b) : b = (c – d) : d
• Componendo -> a : b = c : d, then (a + b) : b = (c+d) : d
• Alternendo -> a : b = c : d, then a : c = b: d

• Componendo and dividendo

Componendo-dividendo rule is one of the properties of proportion. It reduces the complexity of solving questions related to fractions.

According to this, if  a/b = c/d
Then,                    ( a+b/a-b)= (c+d/c-d)

Also Read: Chain Rule Problems, Direct & Indirect Proportion

Types of Questions Asked From Ratio and Proportion Topic

• When two ratios are given  and we have to find a ratio between three quantities

Simply means, (a*b):(b*b):(b*c)

Q. If a:b = 2:4 and b:c = 4:10 then find a:b:c?

a:b = 2:4

b:c = 4:10

then, (2*4):(4*4):(4*10)

8:16:40

• When three ratios are given  and we have to find a ratio between the four quantities

Simply means, (a*b*c):(b*b*c):(b*c*c):(b*c*d)

Q. If a:b = 2:4 and b:c  = 4:10 and c:d = 3:5 then find a:b:c:d?

a:b= 2:4

b:c =4:10

c:d=3:5

abc:bbc:bcc:bcd

24:48:120:200

• When Quantities are equivalent to each other and we need to find their ratio

  • First, use a constant in order to find the values of individual quantities
  • Once you find them, remove the constant and you will get the answer

Q. If 2X=3Y:5Z then find X:Y:Z?

Taking n as a constant

so, 2X=3Y:5Z = n

Now, getting individual quantities

2X=n

X=n/2,

Similarly,

Y=n/3

Z=n/5

X:Y:Z

n/2:n/3:n/5

1/2:1/3:1/5

When you get the answer, in this situation find the lcm of the denominator and multiply it to eliminate the fraction

So LCM of 2,3,5 is 30

30(1/2):30(1/3):30(1/5)

15:10:6