**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Ratio and Proportion**

Contents

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**Ratio**

Ratio compares two or more things of same kind. If we compare two things, then ratio can be defined as follows Ratio of two quantities is the number of times of one quantity contains another quantity of the same kind.

It is clear that the ratio of two quantities is equivalent to the fraction of one quantity to the other.

If the two quantities are a and b, then ratio of a and b is represented as a/b or a : b.

**Note** (i) a is called antecedent. (1st term = Antecedent)

(ii) b is called consequent. (2nd term = Consequent)

**Different Types of Ratio**

**Duplicate Ratio** This is the ratio of the squares of two numbers. If x and y are two numbers, then duplicate ratio between ‘ them will be x²:y².

**e.g.,** Duplicate ratio of 3 : 4 = 3² : 4² = 9:16

**Sub-duplicate Ratio** This is the ratio of the square roots of two numbers. If the two numbers are x and y, then sub-duplicate ratio between them will be √ x : √ y.

**e.g.,** Sub-duplicate ratio of 4: 9 = √4: √9 = 2 :3

**Compounded Ratio** When two or more ratios are multiplied together, they are said to be compounded ratio. The compounded ratio of a : b and c : d will be ac : bd and a : b , c : d and e : f will be ace : bdf.

**e.g.,** Compounded ratio of 2 :5 and 3:7 is 6 :35.

**Example Two numbers are in the ratio 3 : 4. Their LCM is 84. The greater number is SSC(1o+2) 2010**

(a) 21

(b) 24

(c) 28

(d) 84

**Example Two natural numbers are in the ratio 3 : 5 and their product is 2160. The smaller of the numbers is SSC (10 + 21 2010**

(a) 36

(b) 24

(c) 18

(d) 12

**Example What must be added to each term of the ratio 7 : 11, so as to make it equal to 3 : 4? ssc (10+2) 2010**

(a) 8

(b) 7.5

(c) 6.5

(d) 5

**Relation Among More Than Two Quantities**

**(i) For Three Quantities** if A:B = x1:y1 and B : C =x2:y2, then the ratio of

A:B:C = (x1 x x2):(y1 x x2):(y1 x y2)

**(ii) For Four Quantities **If A:B = N1:D1, B:C=N2:D2 and C:D = N3:D3,

= Then, A:B:C= N1N2N3: D1N2N3: D1D2N3: D1D2D3

**Example If 1/3 0f A = 75% of B= 0.6 of C, then A: B: C is SSC (10 + 2) 2012**

(a) 4 : 5 : 9

(b) 5 : 9 : 4

(c) 9 : 5 : 4

(d) 9 : 4 : 5

**Rules Related to Ratio**

There are some important rules related to ratio which are given below

**Rule I** If the two numbers are in the ratio of a1 : a2 and the sum of these numbers is A, then these numbers will be a1A/a1+a2 and a2A/a1+a2 , respectively.

or

If a mixture of AL; two liquids P and Q are in the ratio of a1 : a2, then the quantities of liquids P and Q in the mixture will be a1A/a1+a2 L and a2A/a1+a2 L, respectively.

**Example If Rs 1000 is divided between A and B in the ratio 3 : 2, then A will receive ssc (10+2) 2010**

(a) Rs 400

(b) Rs 500

(c) Rs 600

(d) Rs 800

**Rule II** If three numbers are in the ratio of a1 : a2 : a3 and the sum of these numbers is A, then these numbers will be

**Proportion**

The equality of two ratios is called proportion.

A proportion is an equation that has two equivalent ratios on either side.

In other words, if a/b=c/d then a, b, c and d are said to be in proportion. This equality of ratios is denoted as a : b: : c: d or a : b = c: d.

Here, a is the first term, b is the second term, c is the third term and d is the fourth term. First and fourth terms are called extremes, i.e., a and d, while the second and third terms are called means or middle terms, i.e., b and c.

If quantities a, b, c and d are in proportion, then a/b=c/d

=> a x d = b x c

i.e., Product of extreme terms = Product of middle terms

**Properties of Proportion**

**Reference Corner**

**1. By increasing the price of entry ticket to a fair in the ratio 3:5, the number of visitors to the fair has decreased in the ratio 7:2. In what ratio has the total collection increased or decreased? SSC (10 + 2) 2017**

(a) Increased in the ratio 10 : 21

(b) Increased in the ratio 6:35

(c) Decreased in the ratio 21 : 10

(d) Decreased in the ratio 35:6

**Answer:**

(c)

**2. In a business A and C invested amounts in the ratio 2:1, whereas A and B invested amounts in the ratio 3 : 2. If their annual profit be Rs 157300, then B’s share in the profit is SSC (10+2) 2015**

(a)Rs 36300

(b)Rs 48000

(c)Rs 24200

(d)Rs 48400

**Answer:**

**3. Two numbers are in the ratio of 2 : 3. If their sum is 125, find the numbers. SSC (10+2) 2014**

(a) 20, 30

(b) 32,78

(c) 50, 75

(d) 24, 36

**Answer:**

**4. A box contains 280 coins of Rs 1, 50 paise and 25 paise. The values of each kind of the coins are in the ratio of 8 : 4 : 3. Then, the number of 50 paise coins is SSC (10 + 2) 2014**

(a) 80

(b) 90

(c) 70

(d) 60

**Answer:**

**5. Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The small number is SSC (10 + 2) 2014 .**

(a) 27

(b) 33

(c) 49

(d) 55

**Answer:**

**6. If x : y = 5 : 2, then (8x + 9y): (8x + 2y) is SSC (10 + 2) 2014**

(a) 22 : 29

(b) 26 : 61

(c) 29 : 22

(d) 61: 26

**Answer:**

**Practice Exercise**

**1. A, B and C purchased the mangoes in a ratio 5:3:2. If the difference of mangoes of A and C is 60, find out the total number of mangoes purchased by them**

(a) 200

(b) 150

(c) 250

(d) 300

**2. On a certain railway the first and second class fares are 7 paise per km and 3 paise per km respectively. A man who travelled 100 km spent Rs 3.40 in going part of distance by first class and then in second class. How many kilometre did he travelled in first class?**

(a) 30 km

(b) 48.5 km

(c) 10 km

(d) 51.5 km

**3. A contractor took a contract for building 12 km road in 15 days and employed 100 labours on the work. After 9 days he found that only 5 km road had been constructed. How many more labours should be employed to ensure that the work may be completed with in the given time?**

(a) 120

(b) 90

(c) 110

(d) 100

**4. The ratio between the annual incomes of Arav and Bishu is 4 : 3 and between their annual expenditures is 3 : 2. If at the end Of a year both save Rs 600 each. The difference in their income is**

(a)Rs 450

(b)Rs 500

(c)Rs 600

(d)Rs 750

**5. If the positions of the digits of a two digit number are interchanged, the number newly formed is smaller than the original number by 45. Also, the ratio of the new number to the original number is 3 : 8. What is the original number?**

(a) 61

(b) 72

(c) 94

(d) Can’t be determined

**6. The ratio of 1st and 2nd classes train fairs between two stations is 3 : 1 and that of the number of passengers travelling between these stations by 1st and 2nd classes is 1 : 50. If on a particular day, Rs 2650 be collected from the passengers travelling between these stations, then find the amount collected from 2nd class passengers **

(a) Rs 3000

(b) Rs 3500

(c) Rs 2800

(d) Rs 2500

**7. A contractor employed 25 labourers on a job. He was paid Rs 275 for the work. After retaining 20% of this sum, he distributed the remaining amount amongst the labourers. If the number of men to women labourers was in the ratio 2 : 3 and their wages in the ratio 5:4. What wages did a woman labourer get?**

(a) Rs 10

(b) Rs 8

(c) Rs 12

(d) Rs 15

**8. The students in three batches at a coaching centre are in the ratio 2 : 3 : 5. If 20 students are increased in each batch, the ratio changes to 4 : 5 : 7. The total number of students in the three batches before the increase were**

(a) 10

(b) 90

(c) 100

(d) 150

**9. Rs 2250 is divided among three friends Aman, Bijoy and Chandra in such a way that 1/6 th Aman’s share,1/4th of Bijoy’s share and 2/5th of Chandra’s share are equal. Find Aman’s share**

(a)Rs 720

(b)Rs 1080

(c)Rs 450

(d)Rs 1240

**10. After an increment of 7 in both the numerator and denominator, a fraction changes to 3/4. Find the original fraction**

(a) 5/12

(b) 7/9

(c) 2/5

(d) 3/4

**11. Three men rent a farm for Rs 7000 per annum. A puts 110 cows in the farm for 3 months, B puts 110 cows for 6 months and C puts 440 cows for 3 months. What percentage of the total expenditure should A pay?**

(a) 20

(b) 14.28

(c) 16.66

(d) 11.01

**12. If 391 bananas were distributed among three monkeys in the ratio 1/2 : 2/3: 3/4, how many bananas did the first monkey get?**

(a) 102

(b) 108

(c) 112

(d) 104

**13. A beggar had 10 paise, 20 paise and Rs 1 coins in the ratio 10 : 17 : 7 respectively at the end of the day. If that day he earned a total of Rs 57, how many 20 paise coins did he have? **

(a) 114

(b) 171

(c) 95

(d) 85

**14. In co-education school there are 15 more girls than boys. If the number of girls in increased by 10% and the number of boys is also increased by 16%, there would be 9 more girls than boys. What is the number of students in the school?**

(a) 465

(b) 265

(c) 350

(d) 625

**15. In a small village, there are 4 men for every 3 women and 5 children for every three men. How many children are there in the village if it has 531 women?**

(a) 454

(b) 1180

(c) 1070

(d) 389

**16. A purse contains Rs 1, 50 paise, 25 paise and 20 paise coins in the ratio of 1 : 2 : 4: 5. If the total value of coins is Rs 400, then the number of 20 paise coins exceeding those of 25 paise coins is**

(a) 100

(b) 200

(c) 400

(d) 500

**17. A tea producer blends two quantities of tea from two different gardens, one costing Rs 26/kg and the other 30/kg, in the ratio 5 : 3. He sells the blended tea of Rs 30.25/kg. Find his percentage profit.**

(a) 10%

(b) 12.25%

(c) 20%

(d) 22.50%

**18. A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black pair 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 pair of socks in the original order was**

(a) 4 : 1

(b) 2 : 1

(c) 1 : 4

(d) 1 : 2

**19. If in an agricultural farm, there are 3618 trees consisting of cashewnut trees, mango trees and coconut trees in the ratio 1:3:5, the number of mango trees in the plantation is**

(a) 1814

(b) 1342

(c) 1206

(d) 1196

**Answers**

**Hints & Solutions**

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