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Knowledge in Arithmetic
MATRICES
Sharing the notes of MATRICES in brief. Watch related videos on this link - https://www.youtube.com/results?search_query=MATRICES+Ajaze+Khan
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Given below are the notes for mathematics students, studying the subject Arithmetic. The document includes topics such as Interest Considerations, SIMPLE INTEREST, COMPOUND INTEREST, NOMINAL AND EFFECTIVE INTEREST RATES, etc. #BITS Pilani
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Given below are the notes for mathematics students, studying the subject Arithmetic. The document includes topics such as Total Amount of Annuity, Present Worth of an Annuity, Perpetuity, etc. #BITS Pilani
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Ratio And Proportion- Basics
Ratio And Proportion- Basics What is Ratio? A ratio is a relationship between two numbers by division of the same kind. The ration of a to b is written as a: b = a / b In ratio a : b , we can say that a as the first term or antecedent and b, the second term or consequent. Example: The ratio 4 : 9 we can represent as 4 / 9 after this 4 is a antecedent and , consequent = 9 Rule of ration : In ratio multiplication or division of each and every term of a ratio by the same non- zero number does not affect the ratio. Different type of ratio problem is given in Quantitative Aptitude which is a very essential topic in banking exam. Under below given some more example for your better practice. Anything we learn in our school days was basics and that is well enough for passing our school exams. Now the time has come to learn for our competitive exams. For this we need our basics but also we have to learn something new. That’s where shortcut tricks and formula are comes into action. What is Proportion? The idea of proportions is that two ratio are equal. If a : b = c : d, we write a : b : : c : d, Ex. 3 / 15 = 1 / 5 a and d called extremes, where as b and c called mean terms. Proportion of quantities the four quantities a, b, c, d said proportion then we can express it a : b = c : d Then a : b : : c : d <–> ( a x d ) = ( b x c ) product of means = product of extremes. If there is given three quantities like a, b, c of same kind then then we can say it proportion of continued. a : b = b : c the middle number b is called mean proportion. a and c are called extreme numbers. So, b2 = ac. ( middle number )2 = ( First number x Last number ). Quiz on ratio and proportion:- 1 If P : Q : R = 2 : 3 : 4 , Then P / Q : Q / R : R / P = ? A. 8: 9: 24 B. 7: 9: 24 C. 4: 6: 15 D. 8: 11: 24 E. None of these 2: If 2P = 3Q = 4R, Then P : Q : R = ? A. 2: 3: 5 B. 2: 3: 4 C. 3: 5: 6 D. 1: 2: 3 E. None of these 3: If P : Q = 2 : 3 , Q : R = 4 : 5 and R : S = 6 : 7 , then P : S = ? A. 18: 25 B. 17: 35 C. 16: 35 D. 8: 11 E. None of these 4:Rama distributes his pencil among his four friends Rakesh, Rahul, Ranjan, and Rohit in the ratio 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 . What is the minimum number of pencils that the person should have? A. 66 B. 64 C. 72 D. 77 E. None of these 5: Two numbers are respectively 40% and 60% more than third number. Find the ration of two numbers ? A. 8: 7 B. 7: 9 C. 9: 11 D. 8: 13 E. None of these 6: Rs 1210 were divided among three person P, Q, R so that P : Q = 5 : 4 and Q : R = 9 : 10. Then R gets the amount. A. 450 B. 400 C. 500 D. 375 E. None of these 7: Share Rs.4200 among joy, sanjay and bijoy in the ration 2 : 4 : 6.Find the amount received by sanjay. A. 1200 B. 1300 C. 1400 D. 1500 E. None of these 8 :Find the mean proportional between given two number that is 64 and 49. A. 45 B. 52 C. 54 D. 56 E. None of these 9: What number has to be added to each term of 3 : 5 to make the ratio 5 : 6 . A. 7 B. 6 C. 8 D. 5 E. None of these 10:Rs. 385 were divided among P , Q , R in such a way that P had Rs 20 more than Q and R had Rs 15 more than P . How much was R’s share? A. 156 B. 145 C. 152 D. 150 E. None of these Answers with Explanation:- 1. P : Q : R = 2 : 3 : 4 . Let P = 2k, Q = 3k, R = 4k. Then, P / Q = 2k / 3k = 2 / 3 , Q / R = 3k / 4k = 3 / 4 R / P = 4k / 2k = 2 / 1. SO, P / Q : Q / R : R / P = 2 / 3 : 3 / 4 : 2 / 1 = 8 : 9 : 24. 2. Let 2P = 3Q = 4R = k , Then , P = k / 2, Q = k / 3 , R = k / 4. SO , P : Q : R = k / 2 : k / 3 : k / 4 = 6 : 4 : 3. 3. (C) 4. Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60. Step 2: Then pencil are distributed in ratio among friends, Rakesh = ( 1 / 2 x 60 ) = 30. Rahul = ( 1 / 3 x 60 ) = 20. Ranjan = ( 1 / 4 x 60 ) = 15. Rohit = ( 1 / 5 x 60 ) = 12. Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x. For minimum number of pencils x = 1 . The person should have atleast 77 pencils. 5.Step 1: Let the third number is A Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B /5. Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7 : 8. 6. P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9. So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40 Sum of ratio terms is = ( 45 + 36 + 40 ) =121. R share of amount is Rs (1210 x 40 / 121) = Rs. 400. 7. Amount received by sanjay. 4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount So, the Amount received by sanjay is 1400. 8. The mean proportion of two numbers is Root of 64 and 49 is √8 x √ 7 = 8 x 7 = 56. So, the mean proportional is 56. 9.Let the number to be added x , Then 3 + x / 5 + x = 5 / 6 6 ( 3 + x ) = 5 ( 5 + x ) x = ( 25 – 18 ) = 7 So , the number to be added is 7 . 10. Let Q gets Rs x. Then We can say P gets Rs (x + 20 ) and R gets Rs ( x + 35) . x + 20 + x + x + 35 = 385 3x = 330 x = 110 . R’s share = Rs ( 110 + 35 ) = Rs 145 .
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Problems
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worksheet
Why are the four consecutive terms in an AP taken
We can take the both a-3d,a-d,a+d,a+3d and a,a+d,a+2d,a+3d as the four consecutive numbers in an AP it actually depends on the type of question and they are namely 1 - If in the question we are only provided with the sum of the four consecutive numbers and we are neither provided with value of a nor with the value of d. In this case we take the four consecutive numbers as a-3d,a-d,a+d,a+3d this is because when we take the sum of four numbers it comes out to be a-d+a-3d+a+d+a+3d = 4a . And this 4a can be equated to the sum and hence we can we find the value of a and can proceed further. 2 - If in the question we are provided with the sum of the four consecutive numbers and we are also provided either with the value of a or with the value of d then we can take the four consecutive numbers as a,a+d,a+2d,a+3d this is because when we sum them up a+a+d+a+2d+a+3d = 4a+6d . And 4a+6d can be equated to the sum and we can find the unknown value it is either of a or d . Thanks for reading
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