**Ratio and proportion** is not just a topic of its own but this topic is seen in many topics of maths. Such as Time and Work, Profit and Loss, Simple Interest and Compound Interest, Average, Percentage, Mixture, and Allegation, etc.

Therefore, from the perspective of **SSC, Bank, and Railways**, this is a very important topic and many types of questions are also made on ratio and proportion.

**What is the Ratio?**

The numbers obtained by dividing any two numbers completely by a number are called ratio. For example, dividing **15:25 by 5 will give 3: 5, here 3: 5 is the final ratio** because they cannot be divided by anyone number after that.

The ratio of two quantities P and Q is written as P: Q. Here, P is known as an antecedent, and Q is known as a

consequent. It can also be said that P: Q =** kP: kQ,** where k is any constant known as constant of proportionality, **k ≠ 0**.

Here P is 15 and Q is 25 and k is 5 that means kP:kQ = 5×3:5×5= 15:25.

**Proportion –** Multiplying any two ratios with each other is called proportion. **Ex** – 5/3 =15/9 = 5×9 = 3×15 =45:45 – 1 : 1**II Example** – 8/3 = X/9 , 8×9 : 3 x X = 72 : 3X , X=72/3 = 24 X=24answer

Mean Proportion – a, b, and c are said to be in continued proportion if a/b: b/c

So, **b2 = ac**. Here, b is known as the mean proportion.

##### Problems on Ratio and Proportion

Many types of questions are formed on Ratio and Proportion such as

###### 1. Salary Based Questions

**#** The ratio of the incomes of Mr. Ajay Singh and Mr. Varun Sharma is 3:5 and the ratio of their expenses is 1:3. Who is saving more?

Solution- **Income = Expenditure + Saving** let 3:5 is 300: 500 means Ajay income is 300 and Varun income is 500 and their expenses is 1:2 means 100 and 200 then **Ajay** saving is 300 – 100 = 200 and** Varun** saving is 500 – 200 = 300

Varun saving is more than Ajay so answer is Varun.

###### 2. Questions Based on Age

**#** The age ratio of A and B is 5:11 and their sum is 96, then what is the age of A?

Solution – sum is 96 means 5x + 11x =96 , 16x = 96, x = 6

then the age of A is 5×6 = 30 and Age of B is 11×6= 66 and their sum is 30+66 = 96

Age of A is 30 answer.

###### 3. Questions Based on Coins and Money

**#** A box contains 1-rupee, 50-paise, and 25-paise coins in the ratio 8: 5 : 3. If the total amount of money in the box is 112.50, the number of 50-paise coins is

Solution – 1 rupess coin ratio is 8 so 1×8=8 rupees, 50 paise ratio is 5 convert in rupees means 50×5 = 2.50 rupees, 25 paise ratio is 3 means 25×3 = 0.75 rupees now, add all money = 8x+2.50x+0.75x = 11.25x which is equal to 112.50

11.25x= 112.50, x= 112.50/11.25= x= 10 tehn the number of 50 paise coins is 5x means **5×10= 50 answer**.

###### 4. Questions based on mixture

Water and milk mixture, copper and iron mixture, gold and silver mixture etc.

###### 5. Question on money sharing

Note – There are not any particular **Formula for Ratio and Proportion**.

Here are Some Ratio and Proportion Problems with Answers. Also, Download All types of 100 Questions in Pdf Format Link is given Below

- In school, there were 1554 students and the ratio of the number of boys and girls was 4 : 3. After a few days, 30 girls joined the school but a few boys left; as a result, the ratio of the boys and girls became 7: 6. The number of boys who left school is

(1)**76**(2) 74 (3) 84 (4) 86

- The ratio of the amount of work done by (x – 1) labors in (x +1) days and that done by (x +1) labors in (x +2) days is 5: 6. Then the value of x is

(1)**16**(2) 15 (3) 17 (4) 14

- In a cricket match, there are three types of tickets say A, B, and C each costing Rs. 1000, Rs. 500 and Rs. 200 respectively. The ratio of the tickets sold by categories A, B, and C is 3: 2: 5. If the total collection from selling the

tickets are Rs 2.5 crore, find the total number of tickets sold?

(1) 5000 (2) 4800 (3)**50000**(4) 52000

- Tom is chasing Jerry. In the same interval of time, Tom jumps 8 times while Jerry jumps 6 times. But the distance covered by Tom in 7 jumps is equal to the distance covered by Jerry in 5 jumps. The ratio of the speed of Tom and Jerry is

(1) 48 : 35 (2) 28 : 15 (3) 24 : 20 (4)**20 : 21**

- In an army selection process, the ratio of selected to unselected candidates was 3: 1. If 80 less had applied and 40 less selected, the ratio of selected to unselected candidates would have been 4: 1. How many candidates had applied for the process?

(1)**480**(2) 960 (3) 240 (4) 1440

- A, B, and C go into business as partners with the agreement that their shares of profit will be in the proportion of their capital is. If A’s capital: B’s capital = 2:3, and B’s capital: C’s capital = 2:5, find their shares in a profit of

Rs. 3250.

(1)**Rs. 520, Rs. 780, Rs. 1950**(2) Rs. 5 40, Rs. 760, Rs. 1950 (3) Rs. 540, Rs. 780, Rs. 1930 (4) Rs. 510, Rs. 750, Rs. 1920

- Two vessels A and B contain mixtures of milk and water in the ratio s 4:1 and 9:11 respectively. They are mixed in the ratio of 3: 2. Find the ratio of milk and water in the resulting mixture.

(1 ) 12 : 25 (2 ) 15 : 37 (3 ) 17 : 19 (4 )**33 : 17**

- If A : B = 1 : 2 , B : C = 3 : 4 , C : D = 2 : 3 and D : E = 3 : 4 , then find A : B : C : D : E

(1) 3 : 8 : 6 : 12 : 16 (2)**3 : 6 : 8 : 12 : 1 6**(3) 3 :16 : 6 : 8 : 12 (4) 3 :12 : 6 : 8 : 16

- Determine the fourth proportional to 9.6 m 7.2 m 28.8 m.

(1 ) 22.6 m (2 )**21.6 m**(3 ) 23.6 m (4 ) 20.6 m

- A sum of Rs. 340.68 is distributed among L, M, and N such that L gets Rs 5.72 more than N, and M gets Rs. 2.24 more than L. N gets

(1)**109**(2) 111.90 (3) 103.56 (4) 119.72

- A sum of Rs. 15525 is divided among Sunil, Anil, and Jamil such that if Rs. 22, Rs. 35 and Rs. 48 be diminished from their shares respectively, their remaining sums shall be in the ratio 7 : 10: 13. What would have been the ratio of their sums if Rs. 16, Rs. 77 and Rs. 37 respectively were added to their original shares?

(1) 9 :15 : 17 (2) 17 : 26 : 35 (3)**36 : 52 : 67**(4) None of these

- An amount of Rs. 380 is to be divided among 5 men, 8 boys, and 4 women such that the ratio of the amount received by the three is in the ratio of 8: 4: 7. What is the share of a woman?

(1)**Rs. 35**(2) Rs. 36.5 (3) Rs. 40 (4) Rs. 32.8

- Rs 600 are divided among A, B, and C so that rs 40 more than 2/5 of A’s share, 20 more than 2/7 of B’s share, and Rs 10 more than 9/17 of C’s share are all equal. A’s share is

(1) 180 (2) 160 (3)**150**(4) 140

- A box contains 280 coins of one rupee
**,**50-paise, and 25-paise. The values of each kind of coins are in the ratio of 8: 4 : 3. Then the number of 50-paise coins is

(1) 70 (2) 60 (3)**80**(4) 90

- A box contains 1-rupee, 50-paise, and 25-paise coins in the ratio 8: 5 : 3. If the total amount of money in the box is 112.50, the number of 50-paise coins is

(1) 80 (2)**50**(3) 30 (4) 42

- There are 480 coins in half rupees, quarter rupees, and 10 paise coins and their values are proportional to 5 : 3: 1. The number of coins in each case is

(1) 100, 200, 180 (2) 50, 30, 400 (3)**150, 180, 150**(4) 300, 90, 90

- The ratio

(1) Rs 3,400 (2) Rs 4,100 (3)**Rs 4,500**(4) Rs 5,000

###### Also Download – Average Questions In Maths- For SSC, Bank, Railway

- The ratio of the incomes of A and B as well as of B and C is 3
**:**2. If one-third of A’s income exceeds one-fourth of C’s income by 1000, what is B’s income in?

(1)**3000**(2) 2500 (3) 3500 (4) 4000

- A person bought some rice and wheat for 380. The ratio of the weight of rice and wheat is 4 : 3 and the price of an equal amount of rice and wheat are in the ratio 5: 6. The rice was bought of worth

(1) 380 (2) 300 (3)**200**(4) 180

- In two types of brass, the ratios of Copper to Zinc are 8:3 and 15:7 respectively. If the two types of brass are melted and mixed in the ratio 5:2 a new type of brass is obtained. The ratio of Copper to Zinc in this new type of

brass is

(1) 3:2 (2) 2:3 (3) 3:4 (4)**5:2**

- The number of students in the three classes is in the ratio 2 : 3: 4. If 12 students are increased in each class, this ratio changes to 8: 11:14. The total number of students in the three classes at the beginning was

(1)**162**(2) 108 (3) 96 (4) 54

- If the square of the sum of two numbers is equal to 4 times of their product, then the ratio of these numbers is

(1) 2 : 1 (2) 1 : 3 (3)**1 : 1**(4) 1 : 2

- A man ordered 4 pairs of black socks and some pairs of brown socks. The price of black socks is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was :

(1) 2 : 1 (2)**1 : 4**(3) 1 : 2 (4) 4 : 1

- . If two-third of A is four-fifth of B, then A: B =?

(1) 5 : 6 (2)**6 : 5**(3) 10 : 9 (4) 9 :10

- 12 monkeys can eat 12 bananas in 12 minutes. In how many minutes can 4 monkeys eat 4 bananas?

(1) 10 (2)**12**(3) 4 (4) 8

- My grandfather was 9 times older than me 16 years ago. He will be 3 times my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was

(1) 3 : 8 (2) 2 : 5 (3) 1 : 2 (4)**1 : 5**

- Three numbers are in the ratio 5: 6: 7. If the product of the numbers is 5670, then the greatest number is

(1) 15 (2) 18 (3)**21**(4) 28

###### Also Download – TIME AND WORK PROBLEMS- QUESTIONS WITH PDF

- The average age of boys in the class is twice the number of girls in the class. The ratio of boys and girls in the class of 50 is 4: 1. The total of the ages (in years) of the boys in the class is

(1) 2000 (2) 2500 (3)**800**(4) 400

- A’s income is Rs. 140 more than B’s income and C’s income is Rs. 80 more than D’s. If the ratio of A’s and C’s incomes is 2 : 3 and the ratio of B’s and D’s incomes is 1: 2, then the incomes of A, B, C, and D are respectively

(1) Rs. 260, Rs. 120, Rs. 320 and Rs. 240 (2) Rs. 300, Rs. 160, Rs. 600 and Rs. 520

(3)**Rs. 400, Rs. 260, Rs. 600 and Rs. 520**(4) Rs. 320, Rs. 180, Rs. 480 and Rs. 360

- A vessel contains 20 litres of acid. 4 litres of acid is taken out of the vessel and replaced by the same quantity of water. Next 4 litres of the mixture is withdrawn, and again the vessel is filled with the same quantity of acid left in the vessel with the quantity of acid initially in the vessel is

(1) 4 : 5 (2) 4 : 25 (3)**16 : 25**(4) 1 : 5