In competitive exams, knowing about Ratio and Proportion is really important. These ideas, which come from basic high school math, are super crucial in the Arithmetic section and even show up in other parts like Data Interpretation. Being good at ratio and proportion isn't just helpful by itself; it's like having a super handy tool to solve problems about similar triangles, mixtures, and claims. Getting the hang of these basics isn't just about understanding one thing; it's like having a key that helps solve lots of different questions in various subjects during competitive exams.
Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal.
The ratio is the comparison between similar types of quantities, it is an abstract quantity and does not have any units.
1. A ratio remains the same if both antecedent and consequent are multiplied or divided by the same nonzero number,
2. Two ratios in their fraction notation can be compared just as we compare real numbers.
3. If two ratios a/b and c/d are equal
4. Key Points to Remember about Ratio:
The compounded ratio of the ratios:
(a : b), (c : d), (e : f) is (ace : bdf)
The equality of two ratios is called proportion i.e. If a/b = c/d, then a, b, c, d are said to be in proportion.
Product of means = Product of extremes
Thus, a : b :: c : d ⇔ (b x c) = (a x d)
If a:b = c:d is a proportion, then
To understand the concept of ratio and proportion, go through the difference between ratio and proportion given here.
S.No  Ratio  Proportion 
1  The ratio is used to compare the size of two things with the same unit  The proportion is used to express the relation of two ratios 
2  It is expressed using a colon (:), slash (/)  It is expressed using the double colon (::) or equal to the symbol (=) 
3  It is an expression  It is an equation 
4  Keyword to identify ratio in a problem is “to every”  Keyword to identify proportion in a problem is “out of” 
The LCM process gets very cumbersome when we have to find the ratio out of multiple ratios.
We have the following simple method for that for a chain of ratios of any length.
Suppose you have the ratio train as follows
⇨ A : B = 1 : 2
⇨ B : C = 2 : 3
⇨ C : D = 5 : 6
⇨ D : E = 7 : 8
If we were to find A : B : C : D : E, then the LCM method would have taken quite a long time which is infeasible in examinations of limited hours.
The short cut is as follows:
A : B : C : D : E can be written directly as:
⇨ 1 × 2 × 5 × 7 : 2 × 2 × 5 × 7 : 2 × 3 × 5 × 7 : 2 × 3 × 6 × 7 : 2 × 3 × 6 × 8
⇨ 70 : 140 : 210 : 252 : 288
The thought algorithm for this case goes as:
To get the combined ratio of A : B : C : D : E, from A : B, B : C, C : D, and D : E
In the combined ratio of A : B : C : D : E.
Ratio Formula  a: b ⇒ a/b 
Proportion Formula  a/b = c/d or a : b :: c : d 
Fourth, Third and Mean Proportional  If a : b = c : d, then:

1. Ratio:
2. Proportion:
3. Fourth Proportional:
4. Comparision of Ratios
5. Duplicate Ratios
6. Variations
Q1: In a library, the ratio of the number of story books to that of nonstory books was 4:3 and total number of story books was 1248. When some more story books were bought, the ratio became 5:3. Find the number of story books bought.
Ans: Option A
Explanation:
Q2: Rs. 8400 is divided among A, B, C and D in such a way that the shares of A and B, B and C, and C and D are in the ratios of 2:3, 4:5, and 6:7 respectively. The share of A is
Ans: Option A
Explanation:
Q3: The ratio of the present age of father to that of son is 7:2. After 10 years their ages will be in the ratio of 9:4. The present ages of the father is
Ans: Option A
Explanation:
Q4: Ajay and Raj together have Rs. 1050. On taking Rs. 150 from Ajay, Ajay will have same amount as what Raj had earlier. Find the ratio of amounts with Ajay and Raj initially.
Ans: Option D
Explanation:
Q5: Price of each article of type P, Q, and R is Rs. 300, Rs. 180 and Rs. 120 respectively. Suresh buys articles of each type in the ratio 3:2:3 in Rs. 6480. How many articles of type Q did he purchase?
a. 8
Ans: Option A
Explanation:
Q6: Divide Rs. 60 in the ratio 1:2 between Mike and John.
Solution: Let Mike’s part be x.
Then John’s part is 2x.
Thus, x+2x = 60
3x = 60
x = (60/3)
x = 20.
Therefore, Mike’s part = x = Rs. 20
John’s part = 3x = Rs. (2*20) = Rs. 40
Q7: Three Jars contain alcohol to water in the ratios 3:5, 1:3, and 1:1. If all the three solutions are mixed, what will be the ratio of alcohol to water in final solution?
Solution: Here we are not given the quantities of the solution in three jars. Only the ratio of alcohol to water is given. If the ratio of the quantity of solution would have been there, we could determine the ratio of alcohol to water in the final solution. Hence, the answer here will be cannot be determined.
Q8: If there are Rs. 495 in a bag in denominations of onerupee, 50paisa, and 25paisa coins which are in the ratio 1:8:16. How many 50 paisa coins are there in bag?
Solution: Assume, you have x numbers of one rupee coin. Now coins are in the ratio 1:8:16. This means that if we have x number of one rupee coins, we have 8x number of 50 paisa coins and 16x number of 25 paisa coins. Here order in which ratios are mentioned in the question is very important. In this case, order is one rupee, 50 paisa and 25 paisa and ratio is 1:8:16. Thus,
Number of 50paisa coins = 8x
Number of 25 paisa coins = 16x
Now,Total money in the bag = Rs. 495
(50 paisa coins divided by 2 to convert into rupee and 25 paisa coins divided by 4 to convert into rupee)
Thus, number of 50 paisa coins = 55*8 = 440
155 videos384 docs722 tests

1. What is a ratio? 
2. What are the types of ratios? 
3. What is a proportion? 
4. What is the difference between ratio and proportion? 
5. What is a simple method to solve ratio & proportion questions? 
155 videos384 docs722 tests


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