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<ins>Practice Problems</ins> Question 1: Five yr ago, the average age of P and Q was 15 yr. Now, the average age of P, Q and R is 20 yr. What would be the age of R after 10 yr? A: 35 yr B: 40 yr C: 30 yr D: 50 yr Question 2: A person’s present age is two - fifth of the age of his mother. After 8 yr, he will be one-half of the age of his mother. How old is the mother at present? A: 32 yr B: 36 yr C: 40 yr D: 48 yr Question 3: Devendra is older by 4 yr to Rajendra. After 16 yr, Devendra will be thrice his present age and Rajendra will be five times, of his present age. How old would Rajendra be after 16 yr? A: 30 yr B: 25 yr C: 24 yr D: 20 yr Question 4: Tarun’s age is the cube of a whole number. It was square of another whole number 2 yr ago. How long he must wait before his age is again the cube of a whole number? A: 2 yr B: 10 yr C: 37 yr D: 39 yr Question 5: Rajan is younger than his father by 20 yr. 5 yr ago his father was 3 times elder than him. Find the present age of his father. A: 25 yr B: 30 yr C: 35 yr D: 36 yr Question 6: A father’s age is one more than 5 times of his son’s age. After 3 yr, the father’s age would be 2 less than four times the son’s age. Find the present age of the father. A: 30 yr B: 40 yr C: 31 yr D: 29 yr Question 7: The ratio between the present ages of A and B is 5:3 respectively. The ratio between A’s age 4 yr ago and B’s age 4 yr hence is 1:1. What is the ratio between A’s age 4 yr hence and B’s age 4 yr ago? A: 1 : 3 B: 2 : 1 C: 3 : 1 D: 4 : 1 Question 8: The average age of 19 boys in a class is 21 yr. If the teacher’s age is included, the average increases to 22 yr. What is the teacher’s age? A: 39 yr B: 41 yr C: 40 yr D: 44 yr Question 9: The sum of the ages of 5 children born at the intervals of 3 yr each is 50 yr. What is the age of the youngest child? A: 4 yr B: 8 yr C: 10 yr D: None of these Question 10: The ratio of A’s and B’s ages is 3 : 2. The product of their ages is 216 yr. Then, the sum of their present ages is, A: 18 yr B: 30 yr C: 36 yr D: 32 yr Answers and Solutions 1:- C Solution: According to the question, (P + Q)/2 – 5 =15 (P + Q)/2 = 20 P + Q = 40 -&gt; Eq.1 And, (P + Q + R)/3 = 20 P + Q + R = 60 -&gt; Eq.2 From Eq.1 and Eq.2, R = 20 yr. Therefore, the age of R after 10 yr from now = 20 + 10 = 30 yr. 2:- C Solution: Let person’s mother present age = x. Then, person’s present age = (2/5)x yr According to the question, after 8 yr, (1/2)(x + 8) = ( (2x/5) + 8) (x + 8)/2 = (2x + 40)/5 5x + 40 = 4x + 80 x = 40 yr. Therefore, present age of person’s mother = 40 yr. 3:- D Solution: Suppose, Rajendra’s age = x yr. Then, Devendra’s age = (x + 4) yr Then, (x + 4) + 16 = 3(x + 4) x + 20 = 3x + 12 2x =8 x = 4 yr. Therefore, Rajendra’s age after 16 yr = x + 16 = 4 + 16 = 20 yr. 4:- C Solution: Let present age of Tarun = 27 yr. Then, age of Tarun, 2 yr back = 27 – 2 = 25 yr. So, the cube of 4, next number to three is 64. Therefore, 64 – 27 = 37 yr So, he must wait for 37 yr for his age to again be the cube of a whole number. 5:- C Solution: Let age of Rajan = x yr. Then, age of his father = y yr. According to the question, x + 20 = y -&gt; Eq.1 Now, 5 yr ago 3(x - 5) = (y - 5) 3x – 15 = y – 5 3x – y = 10 -&gt; Eq.2 Putting the value of y from Eq.1 in Eq.2, we get , 2x = 30 x = 15 yr. By putting the value of x in Eq.1, we get, y = 35 yr. So, the age of Rajan’s father = 35 yr. 6:- C Solution: Let present age of son = x yr. Then, present age of father = (5x + 1) yr. According to the question, 4(x + 3) – 2 = (5x + 1) + 3 12 - 2 – 4 = 5x – 4x x = 6 yr. Therefore, the present age of father = 5x + 1 = 5 x 6 + 1 = 31 yr. 7:- C Solution: Let the present ages of A and B be 5x yr and 3x yr respectively. Now, (5x – 4)/(3x – 4) = 1/1 5x – 4 = 3x + 4 2x =8 x = 4 yr. Therefore, the required ratio is , (5 x 4 + 4)/(3 x 4 – 4) = 24/8 = 3 : 1 8:- B Solution: The average age of 19 boys = 21 yr When teacher comes in the class, then the age becomes 19 boys + 1 teacher = 22 yr Therefore, the age of teacher = Old average + New average = 21 + 20 = 41 yr. 9:- A Solution: Let the ages of the children be x, (x + 3) , (x + 6) , (x + 9) and (x + 12) yr respectively. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 5x + 30 = 50 5x = 20 x = 4 yr. 10:- B Solution: Let the present ages of A and B be 3x yr and 2x yr respectively. Now, 3x X 2x = 216 6x2 = 216 x2 = 216/6 = 36 x = 6 yr. Therefore, sum of their present ages = (3x + 2x) = 5x = 5 x 6 =30 yr.

Test your problem solving skills with practice questions on Problems Based on Ages. Practice questions with detailed solution for SSC CHSL and SSC CGL Exams

Problems based on Age Practice Problems Day 58

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<ins>Practice Problems</ins> Question 1: The age of Rakhi is twelve times that of her daughter Anubha. If age of Anubha is 3 yr, then what is the age of Rakhi? A: 20 yr B: 24 yr C: 30 yr D: 36 yr Question 2: If the present ages of Nandu and Shobit are 20 yr and 24 yr respectively, then find the ratio between the age of Nandu (before 4 yr) and Shobit (after 4 yr). A: 5 : 9 B: 4 : 7 C: 2 : 3 D: 5 : 6 Question 3: The age of the father 4 yr ago was 8 times the age of his son. At present, the father’s age is 4 times that of his son. Find the present age of son. A: 9 yr B: 7 yr C: 14 yr D: 18 yr Question 4: At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 yr, Arun’s age will be 26 yr. What is the age of Deepak at present? A: 12 yr B: 15 yr C: 19 and half yr D: 25 yr Question 5: Present ages of Anupam and Raju are in the ratio 5 : 4, respectively. 3 yr hence, the ratio of their ages will become 11 : 9, respectively. What is Raju’s present age? A: 24 yr B: 27 yr C: 40 yr D: Data inadequate Question 6: A person was asked to state his age. His reply was, ‘Take my age three year hence multiply it by 3 and then subtract three times my age 3 yr ago and you will know how old I am’. What was the age of the person? A: 18 yr B: 20 yr C: 24 yr D: 32 yr Question 7: The age of father is thrice of his son. If the sum of their ages is 48 yr. What is the age of father? A: 30 yr B: 32 yr C: 36 yr D: 40 yr Question 8: Nikhil is 8 yr younger than his brother Rohan. How old will Rohan be when he is twice as old as Nikhil? A: 4 B: 6 C: 8 D: 16 Question 9: The age of Arvind’s father is 4 times his son’s age. If 5 yr ago, father’s age was 7 times of the age of his son at that time, then what is Arvind’s father’s present age ? A: 84 yr B: 70 yr C: 40 yr D: 35 yr Question 10: Rahim and his uncle differ in their ages by 30 yr. After 7 yr , if the sum of their ages is 66 , what will be the age of the uncle ? A: 51 yr B: 49 yr C: 39 yr D: 41 yr Answers and Solutions 1:- D Solution: Let age of Anubha = x yr. Then age of Rakhi = 12x yr. Therefore, age of Rakhi = 12 x 3 = 36 yr. 2:- B Solution: (Age of Nandu - 4) / (Age of Shobit + 4) = (20 – 4)/(20 + 4) = 16/28 = 4 : 7. 3:- B Solution: Let present age of son = x yr Then, present age of father = 4x yr Now, age of father 4 yr ago = (4x – 4) yr Age of son 4 yr ago = (x – 4) yr According to the question, (4x – 4) = 8 (x – 4) 4x – 4 = 8x – 32 4x = 32 – 4 x = 28/4 x = 7 Hence, the present age of son is 7 yr. 4:- B Solution: Let the present ages of Arun and Deepak be 4x yr and 3x yr , respectively. Then, 4x + 6 = 26 4x = 20 X = 5. Therefore, Deepak’s present age = 3x = 3 x 5 = 15 yr. 5:- A Solution: Let the present ages of Anupam and Raju be 5x yr and 4x yr, respectively. After 3yr, age of Anupam = (5x + 3) yr After 3 yr, age of Raju = (4x + 3) yr According to the question, (5x + 3)/(4x + 3) = 11/9 45x + 27 = 44x + 33 x = 33 – 27 = 6 So, present age of Raju = 4 x 6 = 24 yr. 6:- A Solution: Let the present age of the person = x yr. According to the question, 3(x + 3) – 3(x – 3) = x 3x + 9 – 3x + 9 = x x = 18 yr. So, the person is 18 yr old. 7:- C Solution: Let the age of son = x yr. Then, the age of father = 3x yr. Now, 3x + x = 48 4x = 48 x = 12 Therefore, age of father = 3 x 12 = 36 yr. 8:- D Solution: Let age of Nikhil = x yr. Then, age of Rohan = (x + 8) yr. According to the question, x + 8 = 2x x = 8. Therefore, age of Rohan = 8 + 8 = 16 yr. 9:- C Solution: Let age of Arvind = x yr. Then, age of Arvind’s father = 4x yr. According to the question, (4x – 5) = 7(x – 5) 4x – 5 = 7x – 35 3x = 30 x = 10 yr. Therefore, Arvind’s father’s present age = 4 x 10 = 40 yr. 10:- D Solution: Let age of Rahim = x yr. Then, age of Rahim’s uncle = y yr. According to the question, y - x = 30. -&gt;Eq .1 Now, after 7 yr, (x + 7) + (y + 7) = 66 x + y + 14 = 66 x + y = 52 -&gt; Eq.2 On adding Eq.1 and Eq.2, we get , 2y = 82 y = 41 yr. So, the age of Rahim’s uncle = 41 yr.

Problems Based on Ages Problem Practice Questions Day 57

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<ins>Practice Problems</ins> Question 1: Rs 180 is to be divided in a box consist of one rupee, 50 paise and 25 paise coins in the ratio 2:3:4. What is the number of 50 paise coins? A: 60 B: 120 C: 150 D: 180 Question 2 – A boy has a few coins of denominations 50 paise, 25 paise and 10 paise in the ratio 1:2:3. If the total amount of the coin is Rs 6.5 , the number of 10 paise coin is? A: 5 B: 10 C: 15 D: 20 Question 3: A box contains 56 Rs in the form of coins of one rupee , 50 paisa and 25 paisa . The number of 50 paisa coins is double the number of 25 paisa coins and four times the number of one rupee coin. How many 50 paisa coin are there in box ? A: 64 B: 52 C: 36 D: 16 Question 4: A bag contains equal no. of 50 paise, 25 paise, 20 paise and 5 paise coins respectively. If the total value is 40, how many coins of each type are there? A: 50 B: 35 C: 20 D: 40 Question 5: A bag contains 90 coins of 50 paise, Rs 1 and Rs 2 coins, ratio of total value of coins is 3:4:4. Find total money in bag? A: 81.25 B: 82.50 C: 90.50 D: 89.25 Question 6: A bag contains 1 rupee, 50 paise and 25 paise coins. The value of 1rs, 50 paise and 25 paise coins are in the ratio of 5:3:1 respectively. If the total number of coins are 180 then what will be the total value of all coins? A: 114 B: 180 C: 108 D: 136 Question 7: There are 480 coins in half rupees, Quarter rupees and 10 paisa coins and their value are proportional to 5:3:1. The numbers of coins in each case are? A: 100, 200, 180 B: 50, 30, 400 C: 150,180,150 D: 300, 90, 90 Question 8: 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 be the ratio of their sums if Rs 16, Rs 77 and Rs 37 respectively were added to their original shares? A: 9:13:17 B: 18:26:35 C: 36:52:67 D: 16:27:33 Question 9: A man has 3 sons , 2 daughters and a wife . They divided a sum of Rs 19000 among themselves such that each daughter got 1.5 times the amount received by each son and his wife received Rs 600 less than each son. What is the total amount received by three sons together? A: 2800 B: 8400 C: 5600 D: 4800 Question 10: Two businessmen A and B invests in a business in the ratio 5:8. They decided to reinvest 30 % of the profit back into the business. The remaining was distributed among themselves. I share of profit of A is Rs 87500 then how much profit did the business make? A: 227000 B: 250000 C: 375000 D: 325000 <ins>Answers and Solutions</ins>
&nbsp; 1: B, 120 2: C, 15 3: A, 64 4: D, 40 5: B, 82.50 6: C, 108 7: C, 150,180,150 8: C, 36:52:67 9: B, 8400 10: D, 325000 &nbsp;

Test your problem solving skills with Ratio and Proportion questions. Practice questions with detailed solution for SSC CHSL and SSC CGL Exams

Ratio and Proportion | Day 5

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<ins>Practice Problems</ins> Question1: A sum of money is divided among A, B, C, D in the proportion of 7:6:3:5. If B gets 270 Rs more than C , then share of D is ? A: 250 Rs B: 350 Rs C: 450 Rs D: 455 Rs Question 2: A, B and C start a business together. Three times the investment of A equals four times the investment of B and the capital of B is twice that of C. The ratio of share of each in the profit is? A: 8:3:6 B: 3:8:6 C: 3:6:8 D: 8:6:3 Question 3: A, B and C, invest to start a restaurant. The total investment was Rs 3 lakh, B invested Rs 50000 more than A and C invested Rs25000 less than B. If the profit at the end of year was 14400 Rs then what is C’s share of the profit? A: 3600 B: 4800 C: 6000 D: 7200 Question 4: A, B and C started a business by investing 55000 Rs , 65000 Rs and 75000 Rs respectively. A is a working partner and gets 20 % of the profit and remaining is distributed in proportion of their investment. If total profit is Rs 87750, what is the share of A? A: 29000 B: 31000 C: 35500 D: 37350 Question 5: If a sum of money is to be divided among A,B,C such that A’s share is equal to twice B’s share and B’s share is four times C’s share , then their shares are in the ratio ? A: 1:2:4 B: 1:4:1 C: 8:4:1 D: 2:4:1 Question 6: By mistake instead of dividing Rs 117 among A, B and C in the ratio of 1/2 : 1/3 :1/4, it was divided in the ratio 2:3:4 . Who gains the most and by how much? A: A, 28 Rs B: B, 26Rs C: C, 25Rs D: B, 24 Rs Question 7: Rs 2010 are to be divided among A,B and C in such a way that if A gets Rs 5 then B must get Rs 12 and if B gets Rs 4 then C must get Rs 5.50 . The share of C will exceed that of B by? A: 470 B: 210 C: 330 D: 270 Question 8: Rs 3000 is divided between A, B and C , so that A receives 1/3 as much as B and C together and B receives 2/3 as much as A and C together . Find share of C? A: 700 B: 1000 C: 1050 D: 850 Question 9: In a partnership business B’s capital was half of A’s. If after 8 months B withdrew half of his capital and after 2 months more A withdrew ¼ th of his capital, then the profit of A and B will be A: 5:2 B: 10:23 C: 2:5 D: 23:10 Question 10: A and B entered into a partnership investing Rs 16000 and RS 12000 respectively. After 3 months A withdrew Rs 5000 while B invested Rs 5000 more .After 3 months more C joins with a capital of Rs 21000 . The share of B exceeds that of C, out of a total profit of Rs 26400 after one year by? A: 2400 B: 1200 C: 3600 D: 800 <ins>Answers and Solutions</ins>&nbsp;
 1: C: 450 Rs 2: D: 8:6:3 3: B: 4800 4: D: 37350 5: C: 8:4:1 6: C: C, 25Rs 7: D: 270 8: C: 1050 9: D: 23:10 10: C: 3600 &nbsp;

Test your problem solving kills related to ratio and proportion. Practice questions with detailed solution for SSC CHSL and SSC CGL Exams

Ratio and Proportion | Day 4

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<ins>Practice Problems</ins> Question 1: The ratio of present ages of father and his son is 4:1. 5 years ago their ages were 7:1. The present age of the son is? A. 8 B. 7 C. 5 D. 10 Question 2: Amit is 5 years older than Vaibhav at present. After four years the ratio of their ages will be 5:4. What is Amit’s age at present? A. 12 B. 18 C. 16 D. 21 Question 3: The ratio of the age of Ram and Rahim 10 years ago was 1:3. The ratio of their age five year hence will be 2:3. Then the ratio of their present ages is? A. 1:2 B. 3:5 C. 5:3 D. 3:4 Question 4: The ratio of ages of two students is 3:2. One is older to the other by 5 years. What is the age of the younger student? A. 12 B. 8 C. 10 D. 15 Question 5: The ratio between the present ages of father and mother is 3:2 and that of mother and son 3:2. If son's present age is 20 yrs then find the age of the father? A. 40 B. 45 C. 38 D. 50 Question 6: The ratio of the present age of two brothers is 1:2 and 5 years back the ratio was 1:3. What will be the ratio of age after 5 years? A. 1:4 B. 2:3 C. 3:5 D. 5:6 Question 7: At present the ratio of ages of Rahul and Rohit is 6:5 and fifteen years from now the ratio will get changed to 9:8. Rahul’s present age is? A. 20 B. 15 C. 25 D. 30 Question 8: The present age of two people is 36 and 50 years. If after n years the ratio of their age will be 3:4, then the value of n is A. 4 B. 5 C. 6 D. 7 Question 9: 6 years ago, the sum of ages of A and B was 88 years . A’s age 18 years ago is equal to B’s age 6 years ago. Find the age of A two years hence? A. 51 B. 62 C. 58 D. 45 Question 10: The ratio of the ages of P, Q and R is 3:4:6 respectively. If the sum of the age of P and Q is equal to S and the sum of the age of R and S is 78. Then what is the age of Q? A. 18 B. 24 C. 36 D. 27
<h3> <ins> Answers and Solutions </ins></h3>
1) D 2) D 3) B 4) C 5) B 6) C 7) D 8) C 9) C 10) B

Test your problem solving skills for Ratio and Proportion. Practice questions with video solution for SSC CHSL and SSC CGL Exams

Ratio and Proportion | Practice Problem Part 3

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<ins>Practice Problems</ins> Question 1: If there is a reduction in the number of workers in a factory in the ratio 15:11 and an increment in their wage in the ratio 22:25 then the ratio by which the total wage of workers should be decreased as? A.	5:6 B.	6:5 C.	3:7 D.	7:3 Question 2: The ratio of boys and girls in a college is 5:3. If 50 boys leave the college and 50 girls join the college, the ratio becomes 9:7. The number of boys in the college is? A.	300 B.	400 C.	500 D.	450 Question 3: The mean proportion of 1.21 and 0.09 is? A.	3.3 B.	1.1 C.	0.33 D.	1.9 Question 4: Find the third proportional to 10 and 25? A.	52.5 B.	62.5 C.	50.5 D.	45.5 Question 5: If b is the mean proportion of a and c, then (a-b)³ : (b-c)³ equals? A.	a³:b³ B.	a³:c³ C.	a²:c² D.	b²:c² Question 6: Four numbers are in the ratio 1: 2: 3: 4. Their sum is 16. The sum of the first and fourth number is? A.	5 B.	8 C.	10 D.	80 Question 7: The sum of three numbers is 116. The ratio of second to the third number is 9:16 and first to third is 1:4. Find the second no.? A.	30 B.	32 C.	34 D.	36 Question 8: The ratio of number of balls in bags x and y is 2:3. Five balls are taken from bag y and are dropped in bag x. Number of balls are equal in each bag now. The number of balls in each bag now is? A.	45 B.	20 C.	30 D.	25 Question 9: The number to be added to each of the numbers 7,16,43,79 to make the numbers in proportion is? A.	2 B.	3 C.	5 D.	1 Question 10: Ram got twice as marks in ENGLISH as in SCIENCE. His total marks in ENGLISH, SCIENCE AND MATHS ARE 180. If the ratio of his marks in English and Math is 2:3, what is his marks in science ? A.	30 B.	60 C.	72 D.	90 Answers 1) B, 2) C, 3) C, 4) B, 5) A, 6) B, 7) D, 8) D, 9) C, 10) A

Ratio & Proportion | Practice Problems | Part 2 |

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<ins>Practice Questions</ins> Question 1: Two numbers are in the ratio 2:3. If their sum is 125, find the numbers? A.	50,75 B.	24,36 C.	20, 30 D.	32, 78 Question 2: If two numbers are in the ratio 2:3 and the ratio becomes 3:4 when 8 is added to both the numbers , then the sum of two numbers is ? A.	10 B.	40 C.	24 D.	38 Question 3: If 177 is divided into 3 parts in the ratio 1/2: 2/3: 4/5, then the second part is? A.	75 B.	72 C.	45 D.	60 Question 4: If 6A = 11B = 7C, FIND A: B: C A.	66:42:77 B.	77:42:66 C.	42:77:66 D.	7:11:6 Question 5: A:B = 2:5, B:C = 4:3 and C:D = 2:1. What is the value of A:C:D? A.	 6:5:2 B.	7:20:10 C.	8:30:15 D.	16:30:15 Question 6: If 3 numbers are in ratio 3:2:5, such that the sum of the squares is equal to 1862 then which number is the middle one A.	21 B.	35 C.	14 D.	42 Question 7: If a:b = c:d = e:f = 1:2 , then find (3a+5c+7e) : (3b + 5d + 7f ) A.	8:7 B.	2:1 C.	1:4 D.	1:2 Question 8: If m:n = 3:2 then(4m+5n) : (4m-5n) is equal to A.	4:9 B.	9:4 C.	11:1 D.	9:1 Question 9: If x = 1/3 y and y = 1/2 z then x: y: z is equal to A.	3:2:1 B.	1:2:6 C.	1:3:6 D.	2:4:6 Question 10: If A:B = 3:4 , B:C = 5:7 AND C:D = 8:9 ,then A:D is equal to A.	3:7 B.	7:3 C.	21:10 D.	10:21 Answers and Solutions 1) A 2) B 3) D 4) B 5) D 6) C 7) D 8) C 9) C 10) D &nbsp;
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Ratio & Proportion | Practice Problems | Part 1

RATIO A ratio is a relationship between two numbers that define the quantity of the first in comparison to the second. Ratio is of the form –&gt; a:b Properties of Ratio There is no change in ratio if it is multiplied or divided by the same number. For example – consider the ratio 2:7 or we can write it as 2/7. Let's multiply the ratio with 5 -&gt; (2*5)/(7*5) = 10/35 (10/35 = 2/7 , ratio is same ) In addition or subtraction by the same number ratio between two number changes. For example – Let the ratio of two number be - 2/7 If we add 3 to both numerator and denominator - (2+3)/(7+3) = 5/10 = 1/2. So the ratio changes to 1:2 If we subtract 1 from both parts of the ratio - (2-1)/(7-1) = 1/6, So new ratio = ⅙ Various forms in which ratio can be written – <code>Form 1: A/B = 2/7 Or A:B = 2:7</code> A/B = 2/7 =&gt; 7A = 2B When will 7a be equal to 2b 7 x 2 = 2 x 7 So, A = 2 And B = 7 <code>Form 2 – A:B:C = 1/3 :1/4:1/5</code> In This Case We Take Lcm Of Denominator – 3,4 And 5 = 3*4*5 = 60 A:B:C = 60/3 : 60/4 : 60/5 = 20:15:12 (Simplified Form ) <code>Form 3 - 2a = 7b = 9c , Find A:B:C</code> It Is Similar To Form 1 , But Here We Have 3 Characters 2a = 7b = 9c Will Be Equal When We Put A = 7 * 9 , B = 2*9 , C = 2*7 2 x 7x 9 = 7 X 2 X 9 = 9 X2 X 7 A:B:C = 7*9 : 2*9 : 2*7 = 63:18:14 <code>Form 4 - 1/3 A = 1/4 B = 1/5 C , A:B:C = ?</code> In this case A:B:C = 3:4:5 TYPES OF RATIO – DUPLICATE RATIO - Duplicate ratio of A:B = A² : B² TRIPLICATE RATIO - Triplicate ratio of A:B = A³ : B³ RECIPROCAL RATIO - Reciprocal ratio of A:B = B :A SUB DUPLICATE RATIO - Sub duplicate ratio of A:B = √A : √B SUB TRIPLICATE RATIO - Sub triplicate ratio of A:B = ∛A : ∛B COMPOUNDED RATIO - Compound ratio of A:B and C:D = AC : BD 
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 PROPORTION Proportion is an equation that defines that the two given ratios are equal to each other. Ratio and proportion are said to be faces of the same coin. Proportion is denoted by -&gt; :: or = A:B :: C:D OR A/B = C/D PROPERTIES OF PROPORTION – ADDENDO – If A/B = C/D then A+C : B+D SUBTRANDO - If A/B = C/D then A-C = B-D DIVIDENDO - If A/B = C/D then (A-B)/B = (C-D)/D COMPONENDO - If A/B = C/D then (A+B)/B = (C+D)/D ALTERNENDO - If A/B = C/D then A/C = B/D INVERTENDO - If A/B = C/D then B/A = D/C *NOTE* - A:B :: C:D =&gt; A = First Proportional , B = Second Proportional, C = Third Proportional, D = Fourth Proportional. MEAN PROPORTION - Mean Proportion is of the form -&gt; A:B :: B:C , B² = AC EXAMPLES - <code>1) Find the mean proportion of 4, 25.</code> Solution: For mean proportion it is written as 4:b :: b:25 Acc to formulae - b²= 4 x 25 = 100 b = 10 (mean proportion ) <code>2) Find a third proportional of 4,6.</code> Solution: We are given two digits so we can write it as – 4:6:: 6:x We know: b² = ac, 36 = 4x, x = 9 <code>3) Find third proportional of 4,6,8 </code> Solution: It can be written as 4:6 :: x:8 A:B :: C:D =&gt; A/B = C/D =&gt; AD=BC 2x = 4 * 8 = 32 x = 32/2 = 16

This blog is the part of Exam Lounge's 75 Days Study Plan for SSC CHSL 2020 and covers Quantitative Aptitude.

Ratio and Proportion | Formulas & Practice Problems

<h2>RATIO</h2>
The ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other. ( Ref: Oxford dictionary)&nbsp;

Notation: Ratio of two values a and b is written as a:b or a/b or a to b. For instance, the ratio of the number of boys in a class to the number of girls is 6:5. Here, 6 and 5 are not taken as the exact count of the students but a multiple of them, which means the number of boys can be 6 or 12 or 18…etc and the number of girls is 5 or 10 or 15… etc. It also means that for every 11 students, there are 6 boys and 5 girls.

<blockquote>Example 1: Divide Rs. 60 in the ratio 1:3 between Jake and Ron. </blockquote>
<code>Solution: Let Jake’s part be x.</code> <code>Then Ron's part is 3x.</code> <code>Thus, x+3x = 60</code> <code>=&gt; 4x = 60</code> <code>=&gt; x = (60/4)</code> <code>=&gt; x = 15.</code> <code>Therefore, Jake’s part = x = Rs. 15</code> <code>Ron’s part = 3x = Rs. (3*15) = Rs. 45</code> 
<h2>PROPORTION</h2>
A proportion is simply a statement that two ratios are equal. Notation: A proportion is a comparison of two ratios. If a : b = c : d, then a, b, c, d are said to be in proportion and written as a:b :: c:d or a/b = c/d. a, d is called the extremes, and b, c are called the means. For a proportion a:b = c:d, product of means = product of extremes → b*c = a*d.

<blockquote>Example1: In the income statement of Vikas and Naman, the ratio of their income in the year 2019 was 5 : 4. The ratio of Vikas’s income in the year 2019 to that in 2018 is 3 : 5 and the ratio of Naman’s income in the year 2019 to that in 2018 is 3 : 2. If Rs. 10242 is the sum of the income of Vikas and Naman in the year 2019, then find the income of Naman in the year 2018?</blockquote>
 <code>Solution</code> <code>Let the income of Vikas in 2019 and 2018 be 3x and 5x respectively.</code> <code>Let the income of Naman in 2019 and 2018 be 3y and 2y respectively</code> <code>Since the ratio of their income in the year 2018 was 5: 4</code> <code>5x : 2y = 5 : 4</code> <code>2x = y</code> <code>The sum of their incomes in 2019 is Rs. 10242</code> <code>3x + 3y = 10,242</code> <code>9x = 10,242</code> <code>x = 1,138 and y = 2276</code> <code>Naman’s income for the year 2018 = 2y = Rs. 4552</code>

What are basics of Ratio of proporations? What are the different applications of it. How to solve questions quickly for RRB NTPC, RRB Group D, Bank PO, SSC CGL Exams

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RATIO AND PROPORTION