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CA FOUNDATION, PAPER 3, PART A, , Business, Mathematics, (MCQ Based - 40 Marks), , PART B, , Logical Reasoning, (MCQ Based - 20 Marks), , PART C, , Statistics, (MCQ Based - 40 Marks)

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CHAPTER-1, RATIO & PROPORTION, INDICES, LOGARITHM, , hE/d/͗Zd/K, •, , Ratio is a comparison between 2 or more quantities of same kind and having same units by the method, of division., , •, , Ratio is represented as, , •, , Here A is called EƵŵĞƌĂƚŽƌ or ŶƚĞĐĞĚĞŶƚ., , •, , Here B is called ĞŶŽŵŝŶĂƚŽƌ or ŽŶƐĞƋƵĞŶƚ., , •, , Both terms of a ratio can be multiplied or divied by the same term., , A, OR A:B., B, , ™ dzW^K&Zd/K, •, , /ŶǀĞƌƐĞZĂƚŝŽ, (Reciprocal of given Ratios), , A, B, , B, A, , •, , Inverse Ratio of, , •, , ŽŵƉŽƵŶĚĞĚZĂƚŝŽ, (Multiplication of given ratios), , •, , •, , Compounded Ratio of, , A B C D, , , ,, B C D E, =, , A B C D, u u u, B C D E, , =, , A, E, , ƵƉůŝĐĂƚĞZĂƚŝŽ, (Square of given ratio), , •, , Duplicate Ratio of, , A, B, , A2, B2, , 3

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hE/d//͗WZKWKZd/KE, •, , Comparison of two or more ratios is called proportion., , •, , It is denoted by, , •, , Here A and D are called extreme values or ĞdžƚƌĞŵĞƚĞƌŵƐ while B and C are called ŵŝĚǀĂůƵĞƐŽĨŵĞĂŶ, ƚĞƌŵƐ., , A C, A C, = OR : :, B D, B D, , ™ dzW^K&WZKWKZd/KE, •, , KEd/EhWZKWKZd/KE, , •, , Comparison of more than two ratios is called continued proportion., , •, , E.g., , A B C, = = then A, B, C, D are in continued proportion., B C D, , ™ WZ/E/W>^K&WZKWKZd/KE, •, , /EsZdEK, If, , •, , A C, = then, B D, , B D, =, A C, , >dZEEK, If, , A C, A B, = then, =, B D, C D, D C, =, B A, , •, , KDWKEEK, If, , A C, A +B C+D, = then, =, B D, B, D, A, C, =, A +B C+D, , •, , /s/EK, If, , A C, A -B C -D, = then, =, B D, B, D, A, C, =, A -B C -D, , 7

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ϭϬ͘, , >^^tKZ<, ϭ, , Ϯ, , ϯ͘, , The inverse ratio of 11 : 15 is, , ϱ͘, , 15 : 11, , (b), , (c), , 121 : 225, , (d) none of these, , The ratio of two quantities is 3 : 4. If the, antecedent is 15, the consequent is, (a), , 16, , (b) 60, , (c), , 22, , (d) 20, , The ratio of the quantities is 5 : 7. If the, consequent of its inverse ratio is 5, the, antecedent is, , ϳ͘, , ϴ͘, , (b), , 3:2, , 2:3, , ϭϮ͘, , ϭϯ͘, , 5, ϭϰ͘, , ϭϱ͘, , (b) 4 : 3, , (c) 9 : 16, (d) none of these, The sub-duplicate ratio of 25 : 36 is, (a) 6 : 5, (b) 36 : 25, (c) 50 : 72, (d) 5 : 6, The triplicate ratio of 2 : 3 is, (a) 8 : 27, (b) 6 : 9, (c) 3 : 2, (d) none of these, The sub-triplicate ratio of 8 : 27 is, ΀DdWͲDĂƌĐŚͲϭϵ΁, (a) 27 : 8, (b) 24 : 81, (c), , ϵ͘, , 5, , (c) 7, (d) none of these, The ratio compounded of 2 : 3, 9 : 4, 5 : 6 and 8, : 10 is, ΀DdWͲDĂƌĐŚͲϭϵ΁, (a) 1 : 1, (b) 1 : 5, (c) 3 : 8, (d) none of these, The duplicate ratio of 3 : 4 is, (a), , ϲ͘, , 11 : 15, , (a), , (a), ϰ͘, , ϭϭ͘, , (d) none of these, , The ratio compounded of 4 : 9 and the, duplicate ratio of 3 : 4 is, (a), , 1:4, , (b) 1 : 3, , (c), , 3:1, , (d) none of these, , ϭϲ͘, , ϭϳ͘, , ϭϴ͘, , The ratio compounded of 4 : 9, the duplicate, ratio of 3 : 4, the triplicate ratio of 2 : 3 and 9 : 7, is, (a), , 2:7, , (b) 7 : 2, , (c), , 2 : 21, , (d) none of these, , The ratio compounded of duplicate ratio of 4 :, 5, triplicate ratio of 1 : 3, sub duplicate ratio of, 81 : 256 and sub-triplicate ratio of 125 : 512 is, (a), , 4 : 512, , (b) 3 : 32, , (c), , 1 : 12, , (d) none of these, , If a : b = 3 : 4, the value of (2a+3b) : (3a+4b) is, (a) 54 : 25, (b) 8 : 25, (c) 17 : 24, (d) 18 : 25, Two numbers are in the ratio 2 : 3. If 4 be, subtracted from each, they are in the ratio 3 :, 5. The numbers are, (a) (16, 24), (b) (4, 6), (c) (2, 3), (d) none of these, The angles of a triangle are in ratio 2 : 7 : 11., The angles are, (a) (20O , 70O , 90O), (b) (30O , 70O , 80O), O, O, O, (c) (18 , 63 , 99 ), (d) none of these, Division of ` 324 between X and Y is in the, ratio 11 : 7. X & Y would get Rupees, (a) (204, 120), (b) (200, 124), (c) (180, 144), (d) none of these, Anand earns `80 in 7 hours and Promode `90, in 12 hours. The ratio of their earnings is, (a) 32 : 21, (b) 23 : 12, (c) 8 : 9, (d) none of these, The ratio of two numbers is 7 : 10 and their, difference is 105. The numbers are, (a) (200, 305), (b) (185, 290), (c) (245, 350), (d) none of these, P, Q and R are three cities. The ratio of average, temperature between P and Q is 11 : 12 and, that between P and R is 9 : 8. The ratio between, the average temperature of Q and R is, (a) 22 : 27, (b) 27 : 22, (c) 32 : 33, (d) none of these, , 9

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ϭϵ͘, , ϮϬ͘, , If x : y = 3 : 4, the value of x2y + xy2: x3+ y3 is, (a) 13 : 12, (b) 12 : 13, (c) 21 : 31, (d) none of these, If p : q is the sub-duplicate ratio of p–x2: q–x2, then x2 is, (a), , (c), Ϯϭ͘, , ϮϮ͘, , Ϯϯ͘, , Ϯϰ͘, , Ϯϱ͘, , Ϯϲ͘, , Ϯϳ͘, , Ϯϴ., , 10, , p, p+q, , (b), , q, p+q, , pq, p+q, , (d) none of these, , If 2s : 3t is the duplicate ratio of 2s – p : 3t – p, then, (b) p = 6st, (a) p2 = 6st, (c) 2p = 3st, (d) none of these, If p : q = 2 : 3 and x : y = 4 : 5, then the value of, 5px+ 3qy : 10px+ 4qy is, (a) 71 : 82, (b) 27 : 28, (c) 17 : 28, (d) none of these, The number which when subtracted from each, of the terms of the ratio 19 : 31 reducing it to 1, : 4 is, (a) 15, (b) 5, (c) 1, (d) none of these, Daily earnings of two persons are in the ratio, 4:5 and their daily expenses are in the ratio 7 :, 9. If each saves `50 per day, their daily earnings, in `are, (a) (40, 50), (b) (50, 40), (c) (400, 500), (d) none of these, The ratio between the speeds of two trains is, 7 : 8. If the second train runs 400 kms. in 5, hours, the speed of the first train is, (a) 10 Km/hr, (b) 50 Km/hr, (c) 70 Km/hr, (d) none of these, The fourth proportional to 4, 6, 8 is, (a) 12, (b) 32, (c) 48, (d) none of these, The third proportional to 12, 18 is, (a) 24, (b) 27, (c) 36, (d) none of these, The mean proportional between 25, 81 is, (a) 40, (b) 50, (c) 45, (d) none of these, , Ϯϵ͘, , ϯϬ., , ϯϭ͘, , ϯϮ͘, , The number which has the same ratio to 26, that 6 has to 13 is, (a) 11, (b) 10, (c) 21, (d) none of these, The fourth proportional to 2a, a2, c is, (a) ac/2, (b) ac, (c) 2/ac, (d) none of these, If four numbers 1/2, 1/3, 1/5, 1/x are, proportional then x is, (a) 6/5, (b) 5/6, (c) 15/2, (d) none of these, The mean proportional between 12x 2 and, 27y2is, (a) 18xy, (b) 81xy, (c) 8xy, (d) none of these, (Hint: Let z be the mean proportional and z =, , 12x2x27y2, ϯϯ͘, , ϯϰ., , ϯϱ͘, , ϯϲ͘, , ϯϳ͘, , If A = B/2 = C/5, then A : B : C is, (a) 3 : 5 : 2, (b) 2 : 5 : 3, (c) 1 : 2 : 5, (d) none of these, If a/3 = b/4 = c/7, then a + b + c/c is, (a) 1, (b) 3, (c) 2, (d) none of these, If p/q = r/s = 2.5/1.5, the value of ps : qr is, (a) 3/5, (b) 1:1, (c) 5/3, (d) none of these, If x : y = z : w = 2.5 : 1.5, the value of (x + z)/(y +, w) is, (a) 1, (b) 3/5, (c) 5/3, (d) none of these, If (5x – 3y)/(5y – 3x) = 3/4, the value of x : y is, (a) 2 : 9, (b) 7 : 2, (c), , ϯϴ., , ϯϵ͘, , 7:9, , (d) none of these, , If A : B = 3 : 2 and B : C = 3 : 5, then A : B : C is, (a), , 9 : 6 : 10, , (b) 6 : 9 : 10, , (c), , 10 : 9 : 6, , (d) none of these, , If x/2 = y/3 = z/7, then the value of (2x – 5y + 4z)/, 2y is, (a), , 6/23, , (b) 23/6, , (c), , 3/2, , (d) 17/6, , Chapter 1 : Ratio and Proportion, Indices, Logarithms

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ϰϬ͘, , ϰϭ., , ϰϮ͘, , ϰϯ., , ϰϰ͘, , If x : y = 2 : 3, y : z = 4 : 3 then x : y : z is, (a), , 2:3:4, , (b) 4 : 3 : 2, , The mean proportional between 1.4 gms and, 5.6 gms is, , (c), , 3:2:4, , (d) none of these, , (a), , 28 gms, , (b) 2.8 gms, , (c), , 3.2 gms, , (d) none of these, , Division of `750 into 3 parts in the ratio 4 : 5 : 6, is, (a), , (200, 250, 300), , (b) (250, 250, 250), , (c), , (350, 250, 150), , (d) 8 : 12 : 9, , The sum of the ages of 3 persons is 150 years., 10 years ago their ages were in the ratio 7 : 8 :, 9. Their present ages are, (a), , (45, 50, 55), , (b) (40, 60, 50), , (c), , (35, 45, 70), , (d) none of these, , The numbers 14, 16, 35, 42 are not in, proportion. The fourth term for which they will, be in proportion is, (a), , 45, , (b) 40, , (c), , 32, , (d) none of these, , (c), , ϰϲ͘, , ϰϴ., , ϰϵ͘, , ϱϮ͘, , ϱϯ͘, , Dividendo, Alternendo, , a b c, a+b+ c, = = then, is, 4 5 9, c, , If, (a), , 4, , (b) 2, , (c), , 7, , (d) none of these., , Two numbers are in the ratio 3 : 4; if 6 be added, to each terms of the ratio, then the new ratio, will be 4 : 5, then the numbers are, (a), , 14, 20, , (b) 17, 19, , (c), , 18 and 24, , (d) none of these, , a b, = then, 4 5, , If, , (a), , a+4 b-5, =, a-4 b+5, , (b) , , (c), , a-4 b+5, =, a+4 b-5, , (d) none of these, , (b) Componendo, (d) none of these, , a+ 4 b+ 5, =, =, a-4 b-5, , If p/q = r/s = p – r/q – s, the process is called, (a), , Subtrahendo, , (b) Addendo, , (c), , Invertendo, , (d) none of these, , ϱϰ͘, , If a/b = c/d, implies (a + b)/(a – b) = (c + d)/(c –, d), the process is called, (a), , Componendo, , (c), , Componendo and Dividendo, , (d), ϰϳ͘, , ϱϭ͘, , If x/y = z/w, implies y/x = w/z, then the process, is called, (a), , ϰϱ., , ϱϬ͘, , If a : b = 4 : 1 th e n + is, (a), , 5/2, , (b) 4, , (c), , 5, , (d) none of these, , (b) Dividendo, , none of these, , If u/v = w/p, then (u – v)/(u + v) = (w – p)/(w +, p). The process is called, (a), , Invertendo, , (b) Alternendo, , (c), , Addendo, , (d) none of these, , ϱϱ͘, , a, b, , b, a, , If, , x, y, z, =, =, b + c - a c + a -b a + b - c, , (b – c)x + (c – a)y + (a – b)z is, (a), , 1, , (b) 0, , (c), , 5, , (d) none of these, ‰, , 12, 16, *, 20 are in proportion. Then * is, (a), , 25, , (b) 14, , (c), , 15, , (d) none of these, , 4, *, 9, 13½ are in proportion. Then * is, (a), , 6, , (b) 8, , (c), , 9, , (d) none of these, 11

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,KD tKZ<Ͳϭ, ϭ͘, , Ϯ͘, , ϯ͘, , ϰ͘, , ϱ͘, , ϲ͘, , If a : b = 3 : 8 then (7a + 2b) : (7a – 2b) is, (a) 5 : 37, (b) 37 : 5, (c) 21 : 16, (d) 16 : 21, If (3a + 2b) : (3a – 2b) = 9 : 5 then a : b is, (a) 7 : 2, (b) 3 : 2, (c) 7 : 3, (d) 2 : 3, If a : b : c = 2 : 1 : 3 and 2a – 3b + c = 8 then a + b, + c is, (a) 12, (b) 6, (c) 18, (d) 24, If (a2 + b2) : (a2 – b2) = 41 : 9 then (a3 + b3) : (a3 –, b3) is, (a) 5 : 4, (b) 125 : 64, (c) 189 : 61, (d) 41 : 9, If ( 13  x + 13  x ) : ( 13  x – 13  x ) = 5, then x is, (a) 4, (b) 5, (c) 6, (d) 3, 1 a, If ab = 1 then 1  b is, , (a), , ϳ͘, , ϴ͘, , ϵ͘, , 12, , ϭϬ͘, , a 1, b 1, , (b), , 1 b, a 1, , a 1, 1 a, (c), (d), 1 b, 1 b, A car covers a distance of 150 km in 2 hrs and 40, minutes, while a motorcycle covers the same, distance in 2 hours, what is the ratio of their, speeds ?, (a) 3 : 4, (b) 4 : 3, (c) 4 : 5, (d) none, The marks obtained by a student in 3 subject, 1 1 3, a, b and c are in the ratio of : : . If his, 2 3 5, total score is 430 then his marks in c is, (a) 150, (b) 100, (d) none, (c) 180, How many 50, 25 and 10 paise coins of which, the numbers are in the ratio 3 : 4 : 5 are together, worth Rs. 15 ?, , ϭϭ͘, , ϭϮ͘, , ϭϯ͘, , ϭϰ͘, , ϭϱ͘, , ϭϲ͘, , ϭϳ͘, , (a) 9, 12, 15, (b) 12, 16, 20, (c) 15, 20, 25, (d) 3, 4, 5, The ratio of two terms is 1 : 25. If 36 added to, second term then the ratio becomes 1 : 28., The first terms is, (a) 12, (b) 10, (d) 9, (c) 8, Three friends divide ` 391 in three, 1 2 3, proportional parts : : . How much is the, 2 3 4, last share ?, (a) 135, (b) 153, (d) none, (c) 100, What least number must be added to each one, of 6, 14, 18, 38 to make them in proportion ?, (a) 2, (b) 3, (c) 4, (d) none, If A’s money is to B’s money as 4 : 5 and B’s, money is to C’s money as 2 : 3 and C has 1500 `, then A has., (b) 800, (a) 1000, (c) 1200, (d) 2000, A bag contains Rs. 600 in the form of one –, rupee, 50 paise and 25 paise coins in the ratio, 3 : 4 : 12. The number of 25 paise coins is, (a) 900, (b) 800, (c) 1200, (d) 1000, A mixture contains milk and water in the ratio, 5 : 1. On adding 5 litres of water, the ratio of, milk and water becomes 5 : 2. The quantity of, milk in the original mixture is, (a) 25 litres, (b) 20 litres, (c) 30 litres, (d) 15 litres, Out of the ratios 7 : 20, 13 : 25, 17 : 30 and 11 : 15, the largest one is ?, (a) 11 : 15, (b) 7 : 20, (c) 17 : 30, (d) 13 : 25, The incomes of a and b are in the ratio 3 : 2 and, their expenditures in the ratio 5 : 3. If each, saves ` 1500 then B’s income is, (b) 9000, (a) 3000, (c) 6000, , (d) none, , Chapter 1 : Ratio and Proportion, Indices, Logarithms

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ϭϴ͘, , ϭϵ͘, , ϮϬ͘, , Ϯϭ͘, , ϮϮ͘, , Ϯϯ͘, , The ratio compounded of duplicate ratio of 4 :, 5, triplicate ratio of 1 : 3, sub-duplicate rate, of 81: 256 and sub-triplicate ratio of 125 : 512 is, (a) 4:512, (b) 3:32, (d) none, (c) 1:12, P, Q and R are three cities. The ratio of average, temperature between P and Q is 11: 12 and, that between P and R is 9: 8. The ratio between, the average temperature of Q and R is:, ΀DdWͲDĂƌĐŚͲϭϴ΁, (a) 22 : 27, (b) 27: 22, (d) none, (c) 32 : 33, The ratio of the prices of two types of cars was, 16: 23, Two years later when the price of the, first has increased by 10% and that of the, second by Rs. 477, the ratio of the prices, becomes 11 : 20. Find the original prices of the, two types of cars, (b) (748, 1319), (a) (848, 1219), (c) (948, 1119), (d) none, If 2s : 3t is the duplicate ratio of 2s - p : 3t - p,, then, (b) p = 6st, (a) p2 = 6st, (c) 2p = 3st, (d) none, If A : B = 8:15, B : C = 5 : 8 and C : D = 4 : 5, then A, : D is equal to :, (a) 2 : 7, (b) 4 : 15, (c) 8 :15, (d) 15 : 4, If 2A = 3B and 4B = 5C, then A : C is :, (a) 4 : 3, (b) 15 : 8, (c) 8 :15, , Ϯϰ͘, , If, , a, 3, , (a) 7, (c), Ϯϱ͘, , Ϯϲ͘, , 1, 3, , b, 4, , : (p - q)2 ?, (a) (q + p)2/p, 2, , Ϯϳ͘, , Ϯϴ͘, , Ϯϵ͘, , ϯϬ͘, , ϯϭ͘, , ϯϮ͘, , 1, 5, , The ratio between two numbers is 3: 4. If their, l.c.m is 180 the numbers are:, (a) 36, 48, (b) 45, 60, (c) 15, 20, (d) none, What quantity must be added to the terms of, the ratio p + q : p - q to make it equal to (p + q)2, , (d) 48, (c) 36, The salaries of A, B, C are in the ratio 2 : 3 : 5. If, the increments of 15%, 10% and 20% are, allowed respectively in their salaries, then, what will be the new ratio of their salaries?, (a) 3 : 3 : 10, (c) 23 : 33 : 60, , c, abc, , then, is equal to :, 7, c, , (d), , (c) (q - p )/2p, (d) none, 94 is divided into two parts in such a way that, the fifth part of the first and the eighth pan of, the second are in the ratio 3 : 4. The first part is, (a) 27, (b) 30, , (b) 10 : 11: 20, , (d) 3 : 4, , (b) 2, , (b) (q - p)2p, , 2, , ϯϯ͘, , (d) Cannot be determined., Two numbers are respectively 20% and 50%, more than a third number. The ratio of the two, numbers is:, (a) 2 : 5, (b) 3 : 5, (c) 4 : 5, (d) 6 : 7, ` 4850 have been divided among A, B, C such, that if their shares be diminished by ` 15, ` 10, and ` 25 respectively, the remainders are in, the ratio 3 : 4 : 5. Then B’s share is :, (a) ` 1595, (b) ` 1610, (d) ` 1600, (c) ` 1626.66, A sum of money is to be distributed among A., B, C, D in the proportion of 5 : 2 : 4: 3. If C gets `, 1000 more than D, what is B’s share?, (a) ` 500, (b) ` 1500, (c) ` 2000, (d) none, ` 1360 have been divided among A, B, C such, that A gets (2/3) of what B gets and B gets (1/4), of what C gets. Then B’s share is :, (a) ` 120, (b) ` 160, (d) ` 320., (c) ` 240, ` 1980 are divided among A, B, C so that half of, A’s part, one-third of B’s part and one- sixth of, C’s part are equal. Then, B’s part is :, (a) ` 660, (b) ` 360, (c) ` 1080, , (d) ` 540., 13

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ϯϰ͘, , ϯϱ͘, , The fourth proportional to the numbers 60, 48,, 30 is :, (a) 36, (b) 24, (c) 48, (d) none, The ratio of the number of boys and girls in a, college is 7 : 8. If the percentage increase in, the number of boys and girls be 20% and 10%, respectively, what will be the new ratio?, (a) 8:9, (b) 17:18, , ϰϮ͘, , ϰϯ͘, , (c) 21: 22, ϯϲ͘, , ϯϳ͘, , ϯϴ͘, , ϯϵ͘, , ϰϬ͘, , ϰϭ͘, , (d) Cannot be deterthined., The mean proportional between 234 and 104, is :, (a) 12, (b) 39, (c) 156, (d) none, Ratio of earnings of A and B is 4 : 7. If the, earnings of A increase by 50% and those of B, decrease by 25 %, the new ratio of their, earnings becomes 8 : 7. What is A’s earnings ?, (a) ` 21,000, (b) ` 26,000, , ϰϱ͘, , (d) ` 28,000, (d) Data inadequate, The ratio of the number of boys and girls in a, school is 3 : 2. If 20% of the boys and 25% of the, girls are scholarship holders, what percentge, of the students does not get the schoLarship?, (a) 56%, (b) 70%, (c) 78%, (d) 80%, 60 kg of alloy A is mixed with 100 kg of alloy B., If alloy A has lead and tin in the ratio 3 : 2 and, alloy B has tin and copper in the ratio 1: 4, then, the amount of tin in the new alloy is :, (a) 36 kg, (b) 44 kg, , ϰϲ͘, , ϰϳ͘, , (c) 53 kg, (d) 80 kg., The ratio of third proportional to 12 and 30 and, the mean proportional between 9 and 25 is, (a) 2 :1, (b) 5 :1, (c) 7 :15, (d) 9 :14, The prices of a scooter and a T.V. are in the, ratio 7 : 5. If the scooter costs ` 8000 more, than a T.V. set, then the price of a T.V. set is :, (a) ` 20,000, (b) ` 24,000, (c) ` 28,000, , 14, , ϰϰ͘, , ϰϴ͘, , Given that 24 carat gold is pure gold; 18 carat, gold is (3/4) gold and 20 carat gold is (5/6) gold,, the ratio of the pure gold in 18 carat gold to, the pure gold in 20 carat gold is :, (b) 9 : 10, (a) 5 : 8, (c) 15 : 24, (d) 8 : 5, An amount of ` 2430 is divided among A, B and, C such that if their shares be reduced by ` 5,, `10 and.` 15 respectively, the remainder shall, be in the ratio of 3 : 4 : 5. Then, B’s share was, (a) ` 605, (b) ` 790, (c) ` 800, (d) ` 810, A and B are two alloys of gold and copper, prepared by mixing metals in the ratio 7 : 2, and 7 : 11 respectively. If equal quantities of, the alloys are melted to form a third alloy C,, the ratio of gold and copper in C will be :, (a) 5 : 7, (b) 5 : 9, (c) 7 : 5, (d) 9 : 5, A piece of string is 40 centimeters long. It is, cut into three pieces. The longest piece is 3, times as long as the middle-sized and the, shortest pieces is 23 centimeters shorter than, the longest piece. The length of the shortest, piece (in cm) is :, (a) 27 cm, (b) 5 cm, (c) 4 cm, (d) 9 cm, The least whole number which when, subtracted from both the terms of the ratio 6 :, 7 gives a ratio less than 16 : 21 is, (b) 2, (a) 3, (d) 6, (c) 4, If one star equals four circles and three circles, equal four diamonds, then the ratio of star :, diamonds is :, (b) 1/3, (a) 3/16, (c) 3/4, (d) 16/3, If two numbers are in the ratio 6 :13 and their, least common multiple is 312, the sum of the, numbers is, (a) 75, (b) 57, (c) 76, (d) 67, , (d) ` 32,000., Chapter 1 : Ratio and Proportion, Indices, Logarithms

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ϰϵ͘, , ϱϬ͘, , ϱϭ͘, , ϱϮ͘, , ϱϯ͘, , ϱϰ͘, , The third proportional to (a2 - b2) and (a + b)2, is:, ΀DdWͲDĂƌĐŚͲϭϴ΁, , ϱϲ͘, , If q : p is the sub duplicate ratio of q–x2 : p–x2, then x2 is, , (a), , ab, ab, , (b), , ab, ab, , (a), , (c), , (a  b)2, ab, , (d), , (a  b)3, a b, , (c), , In an express train the passenger travelling in, A.C. class, First class and Second class are in, the ratio 1 : 2 : 7. and the rate for each class is in, the ratio 5 : 4 : 2. If the total income from this, train is ` 54000. then the income from the A.C., class is :, (a) ` 10,000, (b) ` 15,000, (d) ` 5,000, (c) ` 7,000, A fraction bears the same ratio to 1/27 as 3/7, does to 5/9. The fraction is :, (a) 7/45, (b) 1/35, (c) 45/7, (d) 5/21, If (a + b) : (b + c) : (c + a) = 6 : 7 : 8 and a + b + c =, 14, then the value of c is :, (a) 8, (b) 7, (c) 6, (d) 12., If the ratio of boys to girls in a class is B, the, ratio of girls to boys is G, then B + G is :, (a) equal to 1, (b) greater than 1, (c) less than 1, (d) none, If the value of :, ; a z b , is :, (a) 3, , ϱϱ͘, , ϱϳ͘, , xa xb, 2ab, +, , when x =, x a x b, ab, , (c) 71 Km/hr., (d) None, The ratio of two quantities is 5:9. If the, antecedent is 25, the consequent is, (a) 9, (b) 45, 40, , (d) None, , pq, , pq, (b), , p-q, , pq, ϱϴ͘, , ϱϵ͘, , ϲϬ͘, , ϲϭ͘, , p+q, , (d) None, , If a : b = c : d = 3 : 5, then what are the values of, ad : bc is, (a) 3:5, (b) 5:3, (c) 1:1, (d) None, The number ________ has same ratio to 7/33, that 8/21 does to 4/9, (a) 2/11, (b) 3/11, (c) 2/21, (d) None, then value of x is, , If 5 =, (a), (c), , 10, 5, , (b) 20, (d), , The highest score in an innings was, , ϲϮ͘, , ϲϯ͘, , ϲϰ͘, , 2, 9, , of the, , 2, , of the, 9, remainder. These score differed by 8 runs., What was the total score in the innings?, (a) 162, (b) 152, (c)142, (d) 1132, The mean proportional between 9 and 25 is –, (a) 16, (b) 10, (c) 15, (d) None, One-third of a number is greater than onefourth of its successor by 1. Find the number., (a) 51, (b) 21, (c) 15, (d) None, 1230 baskets of mangoes were loaded in three, trucks. When unloaded, it was found that 5, 10, and 15 baskets were rotten in the trucks, respectively, but the remaining baskets were, in the ratio of 3:4:5. How many baskets were, loaded initially in 3rd truck?, (a) 575, (b), 515, (c) 565, (d), None, , total score and the next highest was, , (b) 4, , (d) 2, (c) 1, The ratio between the speeds of two trains is, 7 : 8. If the second train runs 400 Kms. in 5, hours, the speed of the first train is, (a) 10 Km/hr., (b) 50 Km/hr., , (c), , p+q, , 15

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ϲϱ͘, , ϲϲ͘, , ϲϳ͘, , ϲϴ͘, , Two vessels contain equal quantity of mixtures, of milk and water in the ratio 5:2 and 6:1, respectively. Both the mixtures are now mixed, thoroughly. Find the ratio of milk to water in, the new mixture so obtained., (a) 3:11, (b) 11:3, (c) 12:13, (d) None, The vessels contain water and milk in the ratio, 1:2 and 2:5 are mixed in the ratio 1:4. The, resulting mixture will have water and milk in, the ratio., (a) 31:74, (b) 31:75, (c) 30:77, (d) None, The sub duplicate ratio of 16:49 is, (a) 4:7, (b) 256:2401, (c) 4:9, (d) None, Duplicate ratio of 4:5 is, (a), , ϲϵ͘, , ϳϭ͘, , ϳϮ͘, , ϳϯ͘, , ϳϰ͘, , 16, , (b) 2:, , 5, , (c) 64:125, (d) None, Triplicate ratio of 3:5 is, (a) 27:125, (b) 9:25, (c), , ϳϬ͘, , 16:25, , 1, 33, , 1, : 53, , ϳϱ͘, , ϳϲ͘, , An employer reduces the number of, employees in the ratio of 9:8 and increases, their wages in the ratio of 14:15. In what ratio, is the wages bill decreased?, (a) 20:22, (b) 20:33, (c) 21:20, (d) None, A, B and C have to distribute Rs. 1,000 between, them, A and C together have Rs. 400 and B and, C Rs. 700. How much does C have?, (a), , ϳϳ͘, , ϳϴ͘, , Rs. 100, , (b) Rs. 200, , (c) Rs. 150, (d) None, The mean annual salary of all employees in a, company is Rs. 25,000. The mean salary of male, and female employees is Rs. 27,000 and Rs., 17,000 respectively. Find the percentage of, males and females employed by the company., (a) 60% and 40%, (b) 75% and 25%, (c) 70% and 30%, (d) 80% and 20%, The fourth proportional to (a2– ab + b2), (a3 +, b3) and (a-b) is equal to _________, (a) a2 + b2, (b) a2 – b2, (c), , 1, , (d) None, , (d) 125:27, , The sub–triplicate ratio 8:125 is, (a) 2:6, (b) 2:5, (c) 5:2, (d) None, The 4th proportion of 6, 8 and 15 is –, (a) 40, (b) 30, (c) 20, (d) None, Two numbers are in the Ratio 5:6. If 5 is, subtracted from each number, the ratio, becomes 4:5. Then the number are:, (a) 20, 30, (b) 20, 25, (c) 25, 30, (d) None, What must be subtracted from each term of, the ratio 27:43 to make it equal to 7:15?, (a) 13, (b) 15, (c) 17, (d) None, There are n ARITHMETIC MEANs between 3, and 31 such that the ratio of 3rd mean to, (n–1)th mean is 1:3, then the value of n is, (a) 12, (b) 15, (c) 13, (d) None, , ---0---0---, , Chapter 1 : Ratio and Proportion, Indices, Logarithms

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E^tZ<z^, , 1., , (b), , 2., , (c), , 3., , (a), , 4., , (c), , 5., , (b), , 6., , (c), , 7., , (a), , 8., , (c), , 9., , (c), , 10., , (a), , 11., , (b), , 12., , (a), , 13., , (b), , 14., , (a), , 15. (a), , 16., , (a), , 17., , (c), , 18., , (d), , 19., , (b), , 20., , (a), , 21., , (a), , 22. (b), , 23., , (b), , 24., , (b), , 25., , (b), , 26., , (c), , 27., , (b), , 28., , (c), , 29. (c), , 30, , (b), , 31., , (c), , 32, , (c), , 33., , (d), , 34, , (b), , 35., , (c), , 36 (c), , 37., , (d), , 38., , (c), , 39., , (b), , 40., , (b), , 41., , (a), , 42, , (b), , 43. (d), , 44, , (c), , 45., , (c), , 46., , (a), , 47., , (d), , 48., , (c), , 49., , (d), , 50. (a), , 51., , (b), , 52., , (c), , 53., , (b), , 54., , (d), , 55., , (d), , 56., , (b), , 57 (c), , 58., , (c), , 59., , (a), , 60., , (b), , 61, , (a), , 62., , (c), , 63., , (c), , 64. (b), , 65., , (b), , 66., , (a), , 67, , (a), , 68., , (a), , 69., , (a), , 70., , (b), , 71. (c), , 72., , (c), , 73., , (a), , 74., , (c), , 75., , (c), , 76., , (a), , 77., , (d), , 78. (b), , 17

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ϵ͘, , ,KD tKZ<ͲϮ, ϭ͘, , Ϯ͘, , ϯ͘, , ϰ͘, , Ratio exists only between quantities of ____, kind., (a) Same, (b), bigger, (c) Smaller, (d), None, 42.5 : 23 is same as, (a) 4 : 1, (b), 2:1, (c) 16 : 1, (d), 80 : 1, Ratio between 25 minutes and 45 seconds, (a) 100 : 3, (b), 5:9, (c) 4 : 5, (d), 3 : 10, The ratio compounded of the Duplicate Ratio, of, , ϱ͘, , ϲ͘, , ϳ͘, , ϴ͘, , 18, , 5 : 6 and the Triplicate Ratio of 3 : 5 is, , (a) 4 : 75, (b), 2 : 15, (c) 9 : 50, (d), 3 : 10, The ratio of numbers is 1:2:3 and sum of their, squares is 504, then the numbers are (a) 6, 12, 18, (b), 3, 6, 9, (c) 4, 8, 12, (d), 5, 10, 15, Aperson on a tour has `9600 for his expense., But the tour was extended for another 16 days,, so he has to cut down his daily expenses by, `20. The original duration of the tour had, been?, (a) 48 days, (b), 64 days, (c) 80 days, (d), 96 days, A bag contans 23 number of coins in the form, of 1 rupee, 2 rupee and 5 rupee coins. The total, sum of the coins is `43. The ratio between 1, rupee and 2 rupees coins is 3:2. Then the, number of 1 rupee coins., (a) 12, (b), 8, (c) 10, (d), 16, A recipe for 4 servings requires salt and pepper, to be added in the ratio of 2:3. If the recipe is, adjusted from 4 to 8 servings, what is the ratio, of the salt and pepper that must now be, added?, (a) 4 : 3, (b), 2:6, (c) 2 : 3, (d), 3:2, , ϭϬ͘, , ϭϭ͘, , ϭϮ͘, , ϭϯ͘, , The ages of A and B are in the ratio 3:1. Fifteen, years hence, the ratio will be 2:1. Their present, ages are, (a) 30 years, 10 years, (b) 45 years, 15 years, (c) 21 years, 7 years, (d) 60 years, 20 years, The first, second and third month salaries of a, person are in the ratio 2:4:5. The difference, between the product of the salaries of first 2, months & last 2 months is 4,80,00,000. Find, the salary of the second month, (a) ` 4,000, (b), `6,000, (c) `12,000, (d), `8,000, If 50 is the third proportional to 8 and X then, the value of X is, (a) 20, (b), 2, (c) 10, (d), 1, If b be the mean proportional between a & c, then, (a) b x b = ac, (b), b = (a + c) / 2, (c) b = a + c, (d), b = (a - c) / 2, If a:b = 4:1, then, (a), (c), , ϭϰ͘, , If, (a), (c), , ϭϲ͘, , (b), (d), , 5/4, None, , x 3, 2x + y, If 2y = 2 , then the value of x -2y is, , (a), (c), ϭϱ͘, , 1, 4/5, , a, b, , is, b, a, , 5, 2, , x + 5 + x -16, x + 5  x -16, 10, 30, , a3 + 3a, 3a2 +1, (a) 8, (c) 6, , If, , (b), (d), , 7, 7.1, , 7, then x equals, 3, (b), (d), , 20, 40, , 91, then ‘a’ equals, 37, (b), 7, (d), None, , Chapter 1 : Ratio and Proportion, Indices, Logarithms

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ϭϳ͘, , ϭϴ͘, , ϭϵ͘, , ϮϬ͘, , Ϯϭ͘, , ϮϮ͘, , Ϯϯ͘, , A Dealer mixes Tea costing `6.92 per kg with, Tea costing `7.77 per kg and sells the mixture, at `8.80 per kg and earns a profit 17.5% on his, Sale Price. In what proportion does he mix, them ?, (a) 1 : 2, (b), 3:2, (c) 3 : 4, (d), 5:3, 20 litres of a mixture contains milk and water, in the ratio 5:3. If 4 litres of this mixture be, replaced by 4 litres of milk, the ratio of milk to, water in the new mixture would be, (a) 2 : 1, (b), 7:3, (c) 8 : 3, (d), 4:3, Three containers have their volumes in the, ratio 3:4:5. They are full of mixtures of milk, and water. The mixtures contain milk and, water in the ratio of (4:1), (3:1) and (5:2), respectively. The contents of all these three, containers are poured into a fourth container., The ratio of milk and water in the fourth, container is, (a) 4 : 1, (b), 15 : 48, (c) 157 : 53, (d), 5:2, What must be added to each of the numbers, 10, 18, 22, 38 to make them proportional:, (a) 5, (b), 2, (c) 3, (d), 9, If one type of rice of cost `13.84 is mixed with, another type of rice of cost `15.54, the mixture, is sold at `17.6 with a profit of 14.6% on selling, price then in which proportion the two types, of rice mixed ?, (a) 3 : 7, (b), 5:7, (c) 7 : 9, (d), None, If 4, x and 9 are in proportional then x is equal, to, (a) 36, (b), 6.5, (c) 6, (d), 24, The ratio of the third proportional to 4 and 6, and the mean proportional between 9 and 25, is (a) 5 : 3, (b), 3:5, (c) 8 : 5, (d), 5:8, , Ϯϰ͘, , Ϯϱ͘, , What least number must be added to each one, 6, 14, 18, 38 to make them in proportion ?, (a) 1, (b), 2, (c) 3, (d), 4, For p, q, r, s > 0 the value of each ratio is, P, q, r, s, =, =, =, q +r r + s s + p p + q, , ΀DdWͲƵŐͲϭϴ΁, , Ϯϲ͘, , (a) 1/2, (b), 1/3, (c) 1/4, (d), 1, Let x, y and z are three positive numbers and P, , Ϯϳ͘, , x+y+z, if (p -x): (p-y): (p-z) = 3:5:7 then the, 2, ratio of x:y:z is, ΀DdWͲƵŐͲϭϴ΁, (a) 4:5:6, (b), 6:5:4, (c) 3:5:7, (d), 7:5:3, For a, b, c > 0 the value of each ratio is, , =, , a, b, c, =, =, b + c c + a a +b, , then find the value of each ratio if, ΀DdWͲKĐƚͲϭϴ΁, , a + b + cz 0, , Ϯϴ͘, , (a), , 1, , (c), , 1, , If, , 2, , (b), , 1, , 4, , (d), , 1, , 3, , p r p r, = = = , the process is called, q s q s, , ΀DdWͲDĂƌĐŚͲϭϵ΁, , Ϯϵ͘, , ϯϬ͘, , (a) Subtrahendo, , (b) Componendo, , (c) Alternendo, , (d) none of these, , If x:y:z = 2: 3:5 if x+ y+ z = 60 ,then the value of, z, ΀DdWͲƉƌŝůͲϭϵ͕KĐƚͲϭϴ΁, (a), , 30, , (b) 15, , (c), , 9, , (d) 12, , The ratio of two numbers is 15: 19. If a certain, number is added to each term of the ratio it, become 8: 9. What is the number added to each, of the ratio?, ΀DdWͲƉƌŝůͲϭϵ΁, (a), , 6, , (b) 15, , (c), , 17, , (d) 23, , 19

Page 21 :
ϯϭ͘, , E^tZ<z^, , a b c, 2a + 3b + 2c, If = = then, is, 3 4 5, 4a-b + 2c, ΀DdWͲƉƌŝůͲϭϵ΁, , ϯϮ͘, , ϯϯ͘, , 1, , A, , 21, , A, , 2, , A, , 22, , C, , 3, , A, , 23, , B, , 4, , C, , 24, , B, , 5, , A, , 25, , A, , 6, , C, , 26, , B, , 7, , A, , 27, , A, , 8, , B, , 28, , A, , 9, , B, , 29, , A, , If x+y, y+z, z+x are in the ratio 6:7:8 and x + y + z, =14 then the value of x is ΀DdWͲKĐƚͲϭϵ΁, , 10 D, , 30, , C, , (a), , 6, , (b) 14/3, , 11 A, , 31, , C, , (c), , 8, , (d) 10, , 12 A, , 32, , B, , 13 D, , 33, , A, , 14 B, , 34, , B, , (a), , 11, 19, , (b), , 17, 9, , (c), , 14, 9, , (d), , 19, 7, , The ratio of the earnings of two persons 3:2. If, each saves 1/5th of their earnings, the ratio of, their savings., ΀DdWͲKĐƚͲϭϵ΁, (a) 2:3, , (b) 3:2, , (c), , (d) 5:4, , 4:5, , The Third Proportional to 15 and 20 is, ΀DdWͲKĐƚͲϭϵ΁, , ϯϰ͘, , (a), , 80/3, , (b) 80, , (c), , 80/7, , (d) 120, , 15 B, 16 B, 17 B, 18 B, 19 C, 20 B, , 20, , Chapter 1 : Ratio and Proportion, Indices, Logarithms