Ratio and Proportion -1.pptx hii uiuubuiio
- 2. What is a Ratio? The ratio is a comparison of two like terms in its simplest form. For example, we can compare the height of Ram and Shyam, We can compare the weight of Ram and Shyam, but we can’t compare the height of Ram to the weight of Shyam. A Ratio is denoted as a:b or a/b where a is the antecedent and b is the consequent. RATIO AND PROPORTION 1
- 3. What is a Proportion? Proportion is an equality between two ratios. i.e. a: b :: c : d Where a, b, c, and d are said to be in proportion. a, b, c and d are referred to as first, second, third and fourth proportional respectively. RATIO AND PROPORTION 1
- 4. Ratio: In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent. Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio. Proportion: If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion. Here a and d are called extremes, while b and c are called mean terms. Product of means = Product of extremes. Thus, a : b :: c : d (b x c) = (a x d). RATIO AND PROPORTION 1
- 5. The ratio of the number of apples to oranges in a box is 5 : 9. If 10 apples are eaten, the ratio becomes 1 : 3. Find the number of oranges in the box. A) B) C) D) 35 45 55 50 Question 1
- 6. Two numbers are in the ratio 1 : 2. If 5 is subtracted from each, the new numbers are in the ratio 1 : 3. The smaller number is: A) B) C) D) 10 20 30 40 Question 2
- 7. If A varies directly with B, when A = 21, B = 7. Find the value of A when B = 5? A) B) C) D) 5 10 15 20 Question 3
- 8. The ages of Ram and Anu are in the ratio 2 : 3. 15 years hence, the ratio of their ages will be in the ratio 3 : 4. Find the present age of Anu. A) B) C) D) 60 45 30 15 Question 4
- 9. If 2 : 3 :: x : 15 then, find the value of x. A) B) C) D) 6 8 10 12 Question 5
- 10. The fourth proportion to 5, 8, 15 is _______. A) B) C) D) 21 22 23 24 Question 6
- 11. A sum of money is to be distributed among L, M, N are in the proportion of 5 : 7 : 6. If M gets Rs. 100 more than N, what is N’s share? A) B) C) D) Rs. 500 Rs. 600 Rs. 700 Rs. 800 Question 7
- 12. Two number are in the ratio 1 : 5. If 10 is added to each, the new numbers are in the ratio 1 : 3. The smaller number is _________. Question 8 A) B) C) D) 10 20 30 40
- 13. What is the least number that must be subtracted from 30, 70 and 190 such that the resultant numbers are in continued proportion? Question 9 A) B) C) D) 8 20 5 10
- 14. In a group of dogs and ducks, the total number of legs is 170 and the number of heads is 54. Find the number of dogs in the group. Question 10 A) B) C) D) 27 24 31 34
- 15. The ages of Arjun and Bharath are in the ratio 8:5. Fourteen years hence, the ratio of ages will be 10:7. Find the age of Arjun six years back. Question 11 A) B) C) D) 50 40 60 30
- 16. The ratio of ages of a mother and daughter is 4:2. The product of their ages is 512. What will be the ratio of their ages after 4 years? Question 12 A) B) C) D) 9:2 9:4 9:5 9:7
- 17. A person was to earn Rs.420 and a free holiday for six weeks’ work. He worked for only 2 weeks and earned Rs.60 and a free holiday. What was the value of the holiday in Rs? Question 13 A) B) C) D) 120 80 60 30
- 18. Anu bought 15 cakes and 25 pizzas, Sonu bought 30 cakes and pizzas in some number. Anu paid Rs. 50 for her purchase and Sonu paid Rs. 100 for his purchase. How many pizzas did Sonu buy? Question 14 A) B) C) D) 20 30 40 50
- 19. A man of height 180 cm casts a shadow 150 cm long. At the same time a lamp post casts a shadow 500 cm long. What is the height of the lamp post in meters? Question 15 A) B) C) D) 5 6 7 8
- 20. In a test, a student scores 2 marks for every correct answer and loses 1 mark for every wrong answer. A student attempts all the 60 questions and scores 60 marks. What is the number of questions that he answered correctly? Question 16 A) B) C) D) 20 30 40 50
- 21. There are two glasses. The volume of second glass is thrice that of the first glass. 2/5th of one glass and 3/7th of the other glass are filled with milk. The remaining in both glasses is filled with water. Both the glasses are emptied into a third vessel. Find the ratio of milk to water in the third vessel. Question 17 A) B) C) D) 37:23 4:3 19:11 None
- 22. Vessel A contains 35 litres of milk and vessel B contains 40 litres of water. 10 litres of milk is taken from vessel A and placed in vessel B. Then, 20 litres of the mixture is taken from vessel B and placed in vessel A. Find the ratio of milk in vessel A to water in vessel B. Question 18 A) B) C) D) 29:24 25:24 27:24 31:24
- 23. In the photo studio, a group of boys arrange themselves for a photograph in such a way that each row of boys above the bottom row contains one boy more than the row just below it. If there are 7 rows in all and a total of 84 boys in the group, how many boys does the bottom row contain? Question 19 A) B) C) D) 7 8 9 10
- 24. A, B and C bought apples (in dozens) in the ratio of 9 : 6 : 4 and ate then over the week in the ratio of 5 : 4 : 2. If A was left with one third of his apples, who was left with the least number of apples? Question 20 A) B) C) D) A B C A&B
- 25. THANK YOU
Editor's Notes
- #5: Answer: B Ratio of apple to orange is 5 : 9 (5x : 9x) After 10 apples are taken out, the ratio becomes 1 : 3 => (5x - 10)/(9x) = (1/3) => 15x - 30 = 9x => x = 5 No. of oranges = 9x = 9(5) = 45.
- #6: Answer: A Ratio of two numbers is 1 : 2 (1x : 2x) After subtracting 5 from each, the ratio becomes 1 : 3. so, (x - 5)/(2x - 5) = (1/3) => x = 10 The smallest number is 1x = 1(10) = 10.
- #7: Answer: C Given that A varies directly with B, A = kB i) 21 = k x 7 => k = 3 => A = 3B ii) A = 3(5) = 15
- #8: Answer: B Let present ages are r - Ram, a - Anu. r : a = 2 : 3 15 years hence it becomes (3/4), (2x +15)/(3x +15) = (3/4) => 8x + 60 = 9x + 45 => x = 15 Present age of Anu (a) = 3x = 3 (15) = 45.
- #10: Answer: D Proportions are given as 5, 8, 15, x ( 5 : 8 :: 15 : x ) We need to find x. Product of extremes = Product of means => 5 * x = 8 * 15 => x = 24
- #11: Answer: B L : M : N = 5 : 7 : 6 (i.e., 5x, 7x, 6x). M gets 100 more than N => 7x - 6x = 100 => x = 100. N’s share is 6x = 6(100) = 600.
- #12: Answer: A Ratio of two numbers is 1 : 5 (1x : 5x). After adding 10 to each, the ratio becomes 1 : 3. -> (x + 10)/(5x + 10) = (1/3) => x = 10. The smallest number is 1x = 1(10) = 10.
- #13: Answer: D Lets assume the least number to be subtracted as x.The resultant must be in continued proportion and it is (30-x)/(70-x) = (70-x)/(190-x)On solving,we will get x=10 or Going from the options would be the other way for doing this problem
- #14: Answer: C Lets assume Dogs as ’A’ and Ducks be ’B’.We will get the equations asA+B=54 and Ducks have two legs and dogs have 4 legs 4A+2B = 170 On solving the two equations we will get the number of Dogs to be 31
- #15: Answer: A Lets assume Arjun’s age as ’A’ and Bharath’s age as ’B’.For present age we will get the equation as, A/B=8/5 Fourteen year hence we will get the equation as (A+14)/(B+14)=10/7 On solving we will get Arjun’s present age as 56. Six years back his age would be 56-6=50 years.
- #16: Answer: C Lets assume Mother age as ’M’ and daughter’s age be ’D’So we will get M/D=4/2 and MD=512 On solving we will get M as 32 and D as 16. Therefore ratio after 4 years would be 36:20 = 9:5
- #17: Answer: A Lets assume the free holiday as X and one week’s wage as Y. Forming equations,420+X=6Y 60+X=2Y On solving this we will get X’s value as 120Rs
- #18: Answer: D Image: View->Notes page We can see in the tabular column all the values for Sonu when compared with Anu is getting doubled. So the number of Pizzas should also be doubled. So, Sonu should have bought 50 Pizzas.
- #19: Answer: B 180cm height----150cm shadow?---------------------500cm shadow (180*500)/150=600cm which is 6 m
- #20: Answer: C For every wrong answer the student loses 3 marks(2 marks of the question+1 mark negative).Lets assume all the 60 questions are correct which means he should have got 120 marks wherein he has got only 60 marks.So the remaining 60 marks are gone since he hasn’t answered correctly. The number of wrong questions will be 60/3=20 questions. So the questions which are correct will be 60-20=40. Alternate method: Let the number of correct answers be x and let the number of wrong answers be y For every correct answer,he gets 2 marks For all correct answers he gets 2x marks For every wrong answer , he loses 1 marks For all wrong answers, he loses 1y marks He got 60 marks 2x-y=60------------(1) Total number of questions is 60 x+y=60-------------(2) Solving (1) and (2) we get x=40 So the number of questions he answered correctly is 40
- #21: Answer: D Image: View->Notes page Let the volume of the first glass be ’v’ and the second glass be ’3v’. The amount of milk and water in both the glasses is as follows :The ratio can be calculated by [(2/5)v+(3/7)3v]/[(3/5)v+(4/7)3v] Solving this we get the answer as 59:81 Ans: none
- #22: Answer: A Image: View->Notes page Before 20 litres was removed from, Vessel B,the ratio of milk and water was 1:4.Therefore in 20 litres removed also the ratio of milk and water should be the same.When 20 litres is divided in the ratio 1:4.Therefore 4 litres of milk and 16 litres of water.ie)20 litres is removed from Vessel B in the second operation. As seen from the table the ratio of milk to water in the end will be 29:24
- #23: Answer: A Image: View->Notes page Before 20 litres was removed from, Vessel B,the ratio of milk and water was 1:4.Therefore in 20 litres removed also the ratio of milk and water should be the same.When 20 litres is divided in the ratio 1:4.Therefore 4 litres of milk and 16 litres of water.ie)20 litres is removed from Vessel B in the second operation. As seen from the table the ratio of milk to water in the end will be 29:24
- #24: Answer: B A B c Bought 9x 6x 4x Ate 5y 4y 2y Its given that 9x-5y=1/3(9x) from which we will get the value of y=6x/5 Apples left out with A will be 9x-6x=3x Apples left out with B will be 6x-4(6x/5)=6x/5=1.2x Apples left out with C will be 4x-2(6x/5)=8x/5=1.6x Hence B is left with least number of Apples.