**What are Ratios?**[**a:b **or **a to b **or **a/b**]

Ratios are the mathematical numbers used to compare two entities which are similar to each other in terms of units. For example, we can compare the **height of student 1** to the **height of student 2**. ** FACT:** Properties/Elements that are not similar cannot be compared. Comparison of non-similar properties does not reveal any details of the entities being compared.

**What are Proportions**: [** a/b = c/d** or **a:b :: c:d** **Ex:** 5/7 = 30/42 ]

**Ratios** compare things similar to each other. The ratios are compared with each other using **proportions**. **Proportion** is an equation to represent that two ratios are equivalent. When **two ratios are the same**, they are said to be proportionate to each other or they are said to be in proportion. Proportions are represented by **‘::’ or ‘=’ sign**. Proportions are primarily used to find missing quantities by using the fact that one ratio is equal to the other.

- (A) 22

(B) 16

(C) 19

(D) 15

**2Q. During our campaign against child labor we have found that in 3 glass making factories A, B, and C there were a total of 33 children aged below 18 were involved. The ratio of male to female in A, B and C were 4:3,3:2 and 5:4 respectively. If the number of female children working in the factories B and C is equal then find a total number of female children working in all factories?**

- (A) 19

(B) 11

(C) 14

(D) 15

**3Q. For any 2 numbers m,n; (m+n):(m-n):mn = 7:1:60. Find the value of 1m : 1/n**

- (A) 4:3

(B) 8:6

(C) 3:4

(D) 7:8

**4Q. Find the value of \(\frac {p^{2} + q^{2}}{r^{2} + s^{2}}\)if p: q :: r:s.**

- (A) \(\frac {1}{4}\)

(B) \(\frac {ps}{rq}\)

(C) \(\frac {1}{9}\)

(D) \(\frac {(p-q)^{2}}{(r-s)^{2}}\)

**5Q. Sometimes ago in a cinema hall, a blockbuster movie was being shown. Due to excessive demand of the show, manager of the cinema hall increased the prices of tickets in all the 3 categories.25% in the first class, 12.5% in the special class and 40% in the balcony. If the collection of one show was Rs.218925, then find the collection from the balcony only given that the ratio of the price of the ticket( increased price) for first class, special class, and the balcony is 5:9:14?**

- (A) 109462.5

(B) 58800

(C) 14400

(D) data insufficient

**6Q. The ratio of the 1\(^{st}\) and 2\(^{nd}\) class train fares between 2 stations is 5:2 and that of a number of passengers traveling between 2 stations is 4:57. If on a particular day Rs1675 is collected from passengers traveling between 2 stations then find the difference between the amount collected from 2\(^{nd}\) class and 1\(^{st}\) class train passengers?**

- (A) 1225

(B) 1175

(C) 705

(D) 1057.5

**7Q. Among 3 stations the ratio of fare of 1\(^{st}\) class, 2\(^{nd}\) class and 3\(^{rd}\) class was 10:16:15 and later on the fare is increased in \(^{st}\) and 2\(^{nd}\) class by 3:5, 8:9 respectively but fare in the 3\(^{rd}\) class train is decreased by 42.84%. If the ratio of number of passenger traveling in 3 classes are in ratio 12:11:14 and total fare collected is Rs 103600 then find total revenue collected from 2\(^{nd}\) class train fare?**

- (A) 39600

(B) 29700

(C) 34650

(D) 24750

**8Q. Mrs. Giri purchased one dozen bangles. One day she slipped on the floor and fell down. What cannot be the ratio of broken to unbroken bangles? **

- (A) 1:2

(B) 1:3

(C) 2:3

(D) 1:3

**9Q. An engine can move at the speed of 20/3 m/s without any wagon attached. Reduction in the speed of the train is directly proportional to the square root of the number of wagons attached to the engine. When there are only 4 wagons attached its speed is (50/9) m/s. The greatest number of wagons with which the engine can move is?**

- (A) 144

(B) 143

(C) 12

(D) 63

**10Q. In a family, there were n people. The expenditure of rice per month in this family is directly
proportional to the 5 times the square of a number of people in the family. If the elder son left the family to study in the USA there was a decrease in consumption of 95Kg rice per month. What is the value of n?**

- (A) 5

(B) 9

(C) 12

(D) 10

**Answer**:

1. B

2. C

3. C

4. D

5. D

6. B

7. A

8. C

9. B

10. D

the square root of the radius of a pearl. The price of a necklace was Rs150 When it had 75 pearls each of radius 1cm. Find the radius of the pearl of a necklace having 100 pearls whose cost is Rs 600.

- (A) 6

(B) 4

(C) 9

(D) 12

**2Q. A and B have to write 810 and 900 pages respectively in the same time period. But A completes his work 3 days ahead time and B completes 6days ahead of time. How many pages did A write per hour if B wrote 21 pages more in each hour?**

- (A) 45

(B) 72

(C) 54

(D) 81

**3Q. In a zoo, there are rabbits and pigeons. If the head is counted, there are 340 heads and if legs are counted there are 1060 legs. How many pigeons are there?**

- (A) 120

(B) 150

(C) 180

(D) 170

**4Q. Revenue collected from 1\(^{st}\) class, 2\(^{nd}\) class and 3\(^{rd}\) class between 2 stations are in the ratio 144:99:112 and fare of these three classes are in the ratio 12:11:7 respectively. If the total number of passengers traveling in the train is 776 but a senior citizen, children below 12yrs do not pay any kind of train fare what can be the minimum number of senior citizen traveling in the train if a senior citizen is 25% more than children below 12yrs.**

- (A) 15

(B) 20

(C) 25

(D) 18

**5Q. Cost price of two books is in the ratio 7:11. cost price of the first book is increased by 62.5% and cost price of the second book is increased by 200rs.now cost price of these two books are in the ratio 3:4.then find cost price of the cheaper book?**

- (A) 329

(B) 336

(C) 350

(D) 385

**6Q. In India, the production of tea is 3 times the production of coffee. If a percent more tea and b percent more coffee were produced, the aggregate amount would be 5c percent more. But if b percent more tea and a percent more coffee were produced the aggregate amount produced would be 3c percent more. What is the ratio a: b?**

- (A) 1:3

(B) 1:2

(C) 2:1

(D) 3:1

**7Q. If a,b,c, are 3 positive integers such that a and b are in the ratio 3:4 while b, and c, are in the ratio 2:1, then which one of the following is a possible value of (a+b+c)?**

- (A) 201

(B) 205

(C) 207

(D) 210

**8Q. How many different pairs (a,b) of positive integers are there such that a≤b, and 1/a + 1/b = 1/9?**

- (A) 3

(B) 2

(C) 4

(D) 5

**9Q. The number of ordered pairs of positive integers (m,n) such that 1/m + 1/n = 1/15 is**

- (A) 10

(B) 2

(C) 4

(D) 9

**10Q.How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 Where n is an odd integer less than 60?**

- (A) 7

(B) 5

(C) 3

(D) 6

**Answer**:

1. C

2. C

3. B

4. B

5. B

6. D

7. C

8. A

9. D

10. C

- (A) 31

(B) 51

(C) 52

(D) 55

**2Q. The owner of local jewellery store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchmen, one at a time. To each, he gave half of the diamonds he had then, besides 2 more. He escaped with one diamond. How many did he steal originally?**

- (A) 40

(B) 36

(C) 24

(D) 32

**3Q. A piece of string is 40cm long, It is cut into 3 pieces. The longest piece is 3 times as long as the middle sized and the shortest piece is 23cm shorter than the longest piece. Find the length of the shortest piece.**

- (A) 27cm

(B) 5cm

(C) 4cm

(D) 9cm

**4Q. Let a,b,c,d and e be integers such that a=6b=12c and 2b=9d=12e. Then which of the following pairs contains a number that is not an integer?**

- (A) (a/27, b/e)

(B) (a/36, c/e)

(C) (a/12, bd/18)

(D) (a/6, c/d)

**5Q. Mogambo has got some money which he can spend completely in buying either 50 mangoes or 40 oranges. If he wants to save 10% of the amount and buy at least 20 oranges, then what is the maximum possible number of mangoes that he can buy?**

- (A) 15

(B) 16

(C) 20

(D) 24

**6Q. Rs.34800 is divided among A,B,C and D in such a way that when A gets Rs1,then B gets 80 paise. When B gets 1 rupee then C gets 1.20 rupees, when C gets 1 rupee then D gets 75 paise .find the share of C in total money?**

- (A) 9600

(B) 7200

(C) 8000

(D) 10000

**7Q. A Company reduces the number of his employees in the ratio of 9:8 and increases their wages in the ratio 14:15. The difference in the amount of the total salary bill which was originally Rs1890 after the above two changes will be?**

- (A) Rs90

(B) Rs100

(C) Rs110

(D) Rs120

**8Q. 6 numbers a,b,c,d,e,f are such that ab=1,bc=1/2,cd=6, de=2 and ef=1/2. What is the value of (ad:be:cf)?**

- (A). 4:3:27

(B). 36:1:9

(C). 81:4:9

(D). 72:1:9

**9Q. A man ordered 4pairs of black socks and some pairs of brown socks. The price of a black pair is double to that of a brown pair. While preparing the bill, the clerk did a mistake and interchanged the number of black and brown pairs and this increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was?**

- (A) 4:1

(B) 2:1

(C) 1:4

(D) 1:2

**10Q. The cost of an article (which is composed of raw materials and wages) was 3 times the value of the raw materials used. The cost of raw materials increased in the ratio 3:7 and wages increased in the ratio 4:9. Find the present cost of the article if its original cost was Rs18.**

- (A) Rs41

(B) Rs30

(C) Rs40

(D) Rs46

**Answer**:

1. C

2. B

3. C

4. D

5. C

6. A

7. A

8. D

9. C

10. A

- (A) 140

(B) 125

(C) 265

(D) 255

**2Q. The duration of a railway journey varies as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of coal used, and inversely as the number carriages in the train. In a journey of 50km in half an hour with 18 carriages, 100kg of coal is required. How much coal will be consumed in a journey of 42 km in 28 minutes with 16 carriages?**

- (A) 64kg

(B) 49kg

(C) 25kg

(D) 36kg

**3Q. In a triangle ABC ,(s-a):(s-b):(s-c)=11:8:7 Where s is semi perimeter and a,b ,c are sides .if the sides are increased by 20%,50% and 100% respectively find the ratio of (s’-a1):(s’-b1):(s’-c1) where a1,b1,c1 are new sides and s’ is new semi perimeter.**

- (A) 18:27:38

(B) 47:29:7

(C) 15:18:19

(D) 11:8:7

**4Q. Income of A and B are in ratio 3:4 and their expenditure are in ratio 4:7 their saving are equal if A save Rs1760 more and B increase his expenditure by Rs880 then their saving are in ratio 7:4 .find the average income of A and B?**

- (A) 9240

(B) 8680

(C) 9680

(D) 9160

**5Q. The ratio of the volume of 3 container is the square root of highest square no. of one digit, 2 digit, and 3 digit respectively. the ratio of milk and water is 4:5, 7: 8, 14:17 respectively in all container. If these are mixed in another container then find the ratio of milk and water in that container?**

- (A) 198:447

(B) 293:352

(C) 293:452

(D) 288:357

**6Q. two candles with same length light up at same time 1\(^{st}\) candle end in 8 hours and 2\(^{nd}\) end in 6hr. the rate of burning is different for both candle, After the start of burning, after how much time ratio of their length will be 3:1.**

- (A) 4hr40min

(B) 5hr40min

(C) 5hr20min

(D) 5hr

**7Q. Between two railway stations the fare of 1\(^{st}\), 2\(^{nd}\), and 3\(^{rd}\) class are in the ratio of 8:6:3. But later on the fare of 1\(^{st}\) and 2\(^{nd}\) class is decreased by 16 \(\frac {2}{3}\)% and 22.22 % respectively. In one year the no. of passengers are in the ratio of 1/3 : 1/5 : 1/4. If total tickets amounting Rs. 94905 are sold then find the fare of 3\(^{rd}\) class.**

- (A) 16875

(B) 18225

(C) 17550

(D) 17820

**8Q. A person spends 36.36% of his income on clothes, food, and education in the ratio 1:3:4. He spends 3/8 part of his income on transport and entertainment in the ratio 4:7 and he deposit rest amount in the bank. If he spends Rs2720 on education find the difference of amount he deposits and spends on entertainment:-**

- (A) Rs280

(B) Rs340

(C) Rs320

(D) Rs640

**9Q. If \(\frac {z}{x-2y}\) = \(\frac {2𝑧+𝑥}{2𝑦}\) = \(\frac {2𝑥}{𝑧}\) then \(\frac {𝑥+𝑦+𝑧}{𝑧}\) =?**

- (A) \(\frac {35}{16}\)

(B) \(\frac {37}{12}\)

(C) \(\frac {44}{18}\)

(D) \(\frac {41}{12}\)

**10Q. (x-2y+8z):(y-3z+4w):(4x+5z-7w)=3:4:7,then Find \(\frac {6𝑥+2𝑦−17w}{w}\) = ?**

- (A) 5

(B) 6

(C) 7

(D) 8

**11Q. 16.66% of x = y/8 = z/7 = w/\(\sqrt {25}\) = \(\frac {9𝑥−13𝑦+𝑘^{2}−11y}{34k}\) find k=?**

- (A) 7, \(\frac {-15}{7}\)

(B) \(\frac {7}{2}\), \(\frac {-11}{2}\)

(C) 9, \(\frac {-17}{7}\)

(D) 7, \(\frac {-17}{7}\)

**Answer**:

1. C

2. A

3. B

4. A

5. B

6. C

7. B

8. C

9. B

10. A

11. A