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Ration and Proportion Cuet

This is a pdf on a topic of maths general test for people who are preparing for cuet exam 2024 after 12th boards

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Niyati Jain
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146 views13 pages

Ration and Proportion Cuet

This is a pdf on a topic of maths general test for people who are preparing for cuet exam 2024 after 12th boards

Uploaded by

Niyati Jain
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Ratio & Proportion, Mixture Alligation, Partnership & Average Ratio of two quantities is the fraction that one a quantity is relative to the other. Ratio of ato bis = ora :b. a, the first term is called antecedent and the second tem b is called consequent. It should be noted that both a and b are of the seme units. é SO Important Note: 2S" a a Wany ratio 5 is given such that > > tora > b, and there is an integer x such that x is. ve, then atx a yg aka box b % b-x b> a a Hany ratio | isgiven such that | ° 2 Solution : Let the number to be subtracted be x 6-x_16 7-x 21" Onsolving, we get x= 2.8 5. Pompo and Rompo are two countries engaged in a war. Pompo possesses 8 tanks and Rompo possesses 11 tanks. They get external support from neighbouring countries, of two tanks each. Which ofthe two countries is supposed tohave a relatively greater increase in strength? Solution : Pompo's strength : Rompo's strength inital Pompo's strength : Rompo's strength (after aid received) = 10: 13 10 8 Bon Therefore, Pompo's strength inoreased ina greater proportion as compared to Rompo's strength. 6, Divide 21,000 between Aand B in the ratio 7:3 Solution : z 3 7: 3implies 75 and 7 of €1,000. ‘Therefore, A gets 700 and B gets $300 54 Ratio & Proportion, Mixture Alligation, Partnership & Average 7. ©1150 is to be divided between A, B and C such that the ratio of share of A to that of Bis equal to 3 2 and the share of B to share of C is equal to 3:4. Find their individual share? Solution : 3 HereA:B=3:2= 5 andB:C= [We take the LCM of the values of the common term {Bover here} e.g. LCM of 2 and 3is6 SoA:B=3:2=9:6andB:C=3 Therefore, A: B:C=9:6:8 1150 can be divided between them as follows, Asshare= “10*9 < e450 sshare = Ja = 11506 share = Sy = €300; . 11508 _ C's share= 3 = 8400 8. Whichisthe greatest among he following fraction? 13,18 11 gy 12 11° 13° 9 Solution: Difference in the numerator and denominator is Zineach case. Aso, te rations ae el more than 1H 9 2. Which of the folowing is the smallest among following fraction? 4 ST 49 3 25° 100° 86' 5 Solution : One way of solving such a problem is to convert sachinio decimalsand hen compare Another way is to either equalize the numerator or denominator of every two fractions that are being compared. 1. Therefore, the greatest fraction is aac Suppose we have £ and | tobe compared, If a=, then the fraction with the higher value of denominator is smaller. If b = d, then the fraction with the lower value of numeratoris smaller. c ane ae ae Oe wa on 700" 25 100 ~ 700 80, og iSeliminated 4 49 14 Now comparing >= with 35> 5 36° 25 49 98 ie 14 $8. $50, % icetiminated. comparing “4 3318, 4 3 5 25 26 so, 14 is tne smatest 10. A, B and C are to be given monthly allowance in year 1996 in the ratio 5:3 - 1. If C's share of such allowance is £1,000, how much did A get for the year ended in December 31, 1996. Solution C'sshare= 21,000 As share : C's share = 5:1 Therefore, A's share (monthly) = 5,000 Ass share for whole year = 5000 x 12 = 760,000 ‘11. Ram, Sham and Pran share profits in the ratio 12:1: 5. If Pran’s share is 712,500, what is the profit of the firm? Solution 5 Pran's share = 12500= + of total profit. --Total profit = “2°07 — 245,000 42. 21,59,000is tobe divided in the ratio :3:3 among A, Band C such that a certain sum of £5,000 from the total is divided n the ratio 2: 3between Aan B before such division is made. What are the shares ofAand B? Solution 25,000 i to bo divided between A and B in ratio. 2:3 {Xe share = 82,000, and B's share = 83,000. Amount left is €1,54,000 and to be divided in the ratio5 :3:3 As share = 77 x 154,000 = 270,000 B's share = = «154,000 = 242,000 C’sshare = = « 154,000 = £42,000 11 As total share "45,000. 272,000 and B’s total share 13. Speed of car‘A’ls twice that of truck B’. Both start from a point Ato point Y. If B'took 3 hr more than ', what is the time taken by 'B? Solution Since distance is constant, speed and time are inversely proportional NE Ratio & Proportion, Mixture Alligation, Partnership & Average 14. 15, 16. 17. Therefore, if ratio of speeds of ‘A’ and B= 2:1, ratio of time taken by ‘A and ‘B'= 1:2 Let's assume the time taken by ‘A’ be X and by 8 be 2x. 2X-X= =X=3 =. Time taken by B= 6 hr. Divide 156i four parts in continuous proportion such that the ratio of sum of first and third part to the ‘sum of second and fourth part is Solution : Continuous proportion means that ratio is in a geometric progression, i. 2 ratio which is like asad : ad?: ad? . is a continuous proportion. If (a + ad?): (ad + ad9)= 1:5 a(t +d): adi +d4=1:5 Siid=4:5 = 5 Ratio = a:8a: 25a: 1264 = a+Sa+25a+125a= 156 = 1562 = 156 =a=i ‘Therefore, four parts are 1, 5, 25 and 125. ‘Two solutions contain alcohol and water in the ratio 32 and 5 : 3. If the two solutions are mixed in ‘equal quantities, what isthe ratio of alcohol to water inthe resulting solution? Solution : Required ratio of alcohol to water B's income is 3 of A's income and 75% of C's income. What is C's income asa percentage of As income? Solution : s Bisincome = 5 of A's income. 4 | Of B'sincome C'sincome = 5 4 5 $ orasincome = 2(A’s income). Required percentage = 200%. In an election there are only 2 candidates, Aand B. A got 59% and won by a majority of 144 votes. What's the total number of votes? 18. 19. NS 5.5 Solution : Agot 59%. Therefore, B got 41%. Difference = 59-41 = 18% 18% = 144 voles 144 Therefore, total voles = [5 100= 800 votes. Out of an inheritance of 780,000, Anil invested 26,000 in shares, 30% of total in land and deposited the rest in 10% fixed deposit for 2 years. What is the gain from the fixed deposit after 2 years? Solution : Amount in fixed deposit = 80000-26000- a x 80000 = 730,000 2 £404 =30000« (1-22) ‘Amount after 2 years = 30000 « (112) = 826,300 Interest = 36,300 ~20,000 = %6,300 ‘Aman has certain number of potatoes out of which 13% were bad, 75% of the rest were sold and he ‘was left with 261. How many potatoes did he have initially? Solution : Let's assume that he had P potatoes initially, ‘Then Number of fresh potatoes = 100-13, =87%and Number of unsold potatoes = 25% of 87% of initial number potatoes, Aman lost 12.5% of his money. After spending 70% of the remainder, he has €210 left with him, How much did he have at the beginning? Solution : Let ‘x’be the actual amount of money. Now, 12.5% = 7 ‘So, money left with him, after losing = = of x and Fe =210-> x 8800 Ratio & Proportion, Mixture Alligation, Partnership & Average oS Exercise x » MA: 8 =3:7 and the sum of Aand Bis 45. Find the value of B. @ 28 (© 315 335 @% 3.4 A fraction bears the same ratio to 7 a8 57 to = The fraction is @ ) © @® Mean proportion between 8 and 72 is @) 4 (b) 40 (©) 16 (@ 32 Fourth proportional to 3, 15 and 27 is ale ole ele ola (@ 39 (©) 45 at @ 135 Third proportional to 20 and 30is (a) 40 (&) 45 (c) 60 @ 50 A, B and C join a partnership contributing 2,000, %1,500 and 21,250 respectively. Whats Assshare ina total profit of &3,610? (@ 21,500 (b) 21.520 (c) 21,870 @) %2.290 Astarts a business with &4,000. B joins him after 3months with ¥8,000. C puts a sum of €12,000 in the business for 2 months only. At the end of the ‘year the business gave a profit of 85,200. Find the share of B. (@) 1,500 (&) 22,000 (©) 22,600 (a) 24,000 If ratio of shares of X and Y is 2: 7, what is the ratio of X's share to the difference between Y's and X's shares? @2:7 () 4:12 (2:5 2:9 83,900 is divided among, B and C such that half of As part, one-third of B's part and one-sixth of C's part are equal. Then B's part is (a) %1,080 (b) 260 (c) 1,720 (@) M540 10. 3. 14. 45 16. 1. 18, Inthe above question, whats the ratio of As share tothe difference of B and C’s share? @2:9 2:5 4:5 2:3 ‘Two numbers are in the ratio 5:3. I 9 is subtracted from both of them, they will be in the ratio 23: 12, The first number is @ 45 0) 65 © 5 (@) None of these If ratio of A’s money to B's is 4:5 and B's money to C's is 2: 3, and A has 800, then the total money of A, B, and Cis (a) 72790 (b) 73,000 (©) 73.300 (@ 23.620 Ih4x = 3y = 22, then x: y: zis (a) 4:3:2 (b) 2: ()3:4:2 ()3:4:6 1f68 is divided into two parts such that 7th part of the first is equal to 10th part of the second. The first part is @7 (b) 22 © 2 @ 32 6,800 is to be divided among A, B and C such that A gets two-thirds of what B gets, and B gets ‘one-fourth of what C gets. Find B's share? (@) 1.200 () e300 (©) 1,000 (@ 1,600 9,700 has been divided among X, Y and Z such that if their shares are reduced by €30, £20 and 50, the balance isin the ratio 3 : 4: 5. Whatis Y's share? (@ 33.180 &) BZ (©) %3,25333 (@ 23,200 ‘The sum of 2530 is divided among A, B and C such that A gets @70 more than B, and B gets 780 more thanC. The ratio of Aand Cis (@) 25:18 () 18:10 (5:9 5:2 In aratio equal to 4:9, the antecedent is 36. The consequentis @ 81 (72 (b) 16 (@) None of these Ratio & Proportion, Mixture Alligation, Partnership & Average 19, An amounts distributed amongst, B and C such that A gets half that of B and B gets twice that of C. What is the ratio of B to that of the sum of A and B. (@ 2:5 2:3 (c) 3:2 @)4:3 20. A bag contains 2600 in the form of one-rupee, 50-paisa and 25-paisa coins in the ratio 3 : 4: 12. The number of 25-paisa coins is. (@) 600 (©) 900 (©) 1,200 (@ 1.376 21. In.a mixture of 180 L, the ratio of milk and wateris £1. Ifthe ratio of milk and water is to be 1: 2, the water to be added is (in L) (@) 80L ) 90L (©) 120L (@) 1801, 22, Inamixture of 100 L, the ratio of milk and water is 3: 1. If 200 L of water is added in the mixture, ‘What is the new ratio of milk and water? fa) 1:3 (o) 3:1 (2:5 (@) None of these 23. Out ofa class of 500, boys and girls are equal. In new batch, one-fifth ofthe girls left the class and 25 boys joined in. What is the ratio of boys and iris now? (@) 3:2 () 12:7 (0) 11:8 @ 9:8 24. The population of a country increased by ‘one-tenth and then decreased by one-tenth in two successive years. Ifthe original population was 15,000, what would be the population after 2years? (@) 14,550 () 15.000 (©) 14,850 (@) 16.270 25. The ages of a man and his son are in the ratio 7:2, After 15 years, they would be in the ratio 2:1. The father’s age, when the son was bom, was (@) 25 years (©) 30 years (©) 35 years (@) 42 years 26. Four years aco, father's age was six times that of his son. 12 years from now, father's age will be ‘twice that of the son. The present ratio of ages of father and son is (6:1 (8:2 ) 724 @7:2 5.7 albls fa+bsc) , 27. If 37477 then Se is @7 m2 7 4 > Oz 28. Two whole numbers whose sum is 84 eannot be 34 inthe ratio @9:3 (0) 3:5 © 19:2 @ 5:7 If 0.35 of a number is equal to 0.07 of another umber, the ratio of the number is, @ 1:2 (e) 2:4 (1:5 (424 ‘Two alloys containing copper and iron in the ratios 5: 8and5: 3are melted in equal quantities. The ratio of iron to copper in the resulting alloy is, (@ 103: 105 (b) 15:24 (3:8 (@) 105: 103 80L of amixture of milk and water sin the ratio 5 £3. 1F 16 Lof this mixture is replaced by 16 L of milk, ratio of milk and water becomes @ 2:1 (0) 6:3 7:3 (@) 8:3 The ratio of copper and zinc in a brass piece is, 13:7. How much copper willbe there in 500 kg of such alloy? (@) 300 kg (0) 325 kg (©) 175k (@) 150kg ‘A Band Coin a partnership. Ainvested 216,000 2 for 6 months, B invested 212,000 for year and Cinvested 1,000 for 12 months. Their profit sharing ratio is (@) 8:7:10 (0) 10:8:7 (0) 6:8: 12 (@) None of these ‘A sum of money is divided among A, B and C ‘such that for each rupee that A gets, B gets 65, paise and C gets 35 paise. If C’s share is 7560, the sum is (@) 72400 (0) 22800 (©) %3.200 (@) %3.600 Aratio of two numbers is 2: 3. Whatis the ratio of their squares, ithe two numbers have a difference of 127 @2:3 (©) 9:16 (0) 12:24 @4:9 5.8 36, 37. 38, 398, 40, at 42, 43, Ratio & Proportion, Mixture Alligation, Partnership & Average ‘The cost of providing a product are labour, material and overheads in the ratio 5:7 =. Ifthe profitis calculated as 20% on costs. the ratio of material costs to profit is (a) 5:2 ) 7:3 (3:5 @ 11:9 11,250 is divided among A, B and C so that A receives half as much asB and C together receive; B receives one-fourth of what A and C receive together. The share of Ais more than that of B by (@) $1,500 (©) €3,000 (6) €1,550 (@) 3200 The ratio of boys and gifs ina class of 72is 7:5. How many more girls should be admitted to make equal number of boys and girts? @9 2 (©) 220 (@ 240 ‘The biggest of three positive numbers that are in the ratio 2: 3: 5 and the sum of their squares is. 608, is @s &) 12 (o) 16 (@ 20 In a mixture of 28 L, the ratio of milk and water is 2: 5.12 L of milk is added and § L of water is removed, the new ratiois (a) 9:20 1:4 (co) 3:2 2:3 ‘The incomes of Aand B are in the ratio 3: 2 and their expenses are in the ratio 5 : 3. Ifeach one saves €3,000, then B'sincome is (@) 12,000 (&) %6.000 (c) 79,000 (@ %15,000 ‘A Band Cinvested in partnership with a ratio of 8:7: 5. Awithdraws half of her money after 5 ‘months. Ifthe profit was £26,500 for the yeer, then Bis share is (a) %9,800 () %10200 (c) #10500 (@ e12600 The prices of a bicycle and a rickshaw are in the ratio 5 : 4. If the bicycle costs 800 more than the rickshaw, the price of the rickshaw is (a) 700 (©) %3.200 (©) %4,000 (@) ¥2,400 IA: B::5: 2, the value of 8A + 9B : 8A + 2B is (@) 26:16 () 61:26 (c) 29:22 (@ 22:29 45, If 1 L water is added to 5 L of a 20% solution of sugar in water, what is the strength of the solution now? (@) 16.67% @) 10% (©) 8.33% (@ 12.67% 46. The price of oil is increased by 25%. If the expenditure is not allowed to increase, the ratio of reduction in consumption to regular consumption is @1:3 @) 1:4 @1:5 @ 1:6 47. Three year ago the average age of Abhishek and ‘Aishwarya was 25 year. Now they have a one year ld child. The average age of the family at present iss (@) 25 years (©) 17 years (c) 19 years (@) 28 years 48, Inan ODI cricket match the run rate was only 4.2 inthe first 20 overs. What should be the run rate in the remaining 30 overs to reach the target of 312nuns? @76 () 72 os @ 75 49, A family consists of six members A, B, C, D, E and F. The average age of A and B is 60 years, that of C and Dis 38 years and that of E and F is 10 years. What is the average age of the family? (@) 38 years () 42 years (©) 32 years (@) 36 years 50. Ashopkooper has made a sale of %6,135, 27,227, 26,755, 37,430 and@6,462 for 5 consecutive days. How much sale must he have to make on the sixth day in order to manage an average sales of 26600 over the given six days. (@) 4991 (b) %6054 (© 5601 (@) None of these 51. The average of 50 numbersis zero. How many of them, at the most, can be greater than zero? (@ 49 ©) 2 @o (a 2 52, The average weight of 10 persons increases by 2 kg when a new person comes in place of one of them of weight S6kg. The weight of the new person is (@) 66kg (©) 72kg (©) 76kg (@) 36 kg Ratio & Proportion, Mixture Alligation, Partnership & Average 5.9 53, The average monthly income of Ram and Rahim is &4,500. The average monthly income of Rahim and Salim is 75,500 and the average monthly income of Ram and Salim is 5,100. The monthly income of Ram is (@) 24,100 (©) 24,000 (©) %4,500 (@) %,100 54, A\library has an average of 720 visitors on Sundays ‘and 450 on each of other days of the week. The average number of visitors per day in a month of 58. In a cricket match the run rate was only 4.5 in the first 24 overs. What must be the run scored in the remaining 30 overs to reach the overall run rate of 6? @ 182 ©) 218 © 212 (@ 192 56. A student's marks were wrongly entered as 83 instead of 38. Due to that the average marks for the olass got increased by 0.3. The number of students in the class is: 30 days beginning with Sunday is: @) 100 9 (@) 500 (b) 495 (©) 150 @ 200 (e) 590 (@) 490 cy Answer Key A.(c) 2.(d) 3.(a) 4.(d) 5.(b) 6.(b) 7.(c) 8.(c) 9.(a) 10. (d) 11. (c) 12. (c) 13. (d) 14. (c) 15. (a) 16. (b) 17. (d) 18. (a) 19. (b) 20. (b) 21.(4) 22. (a) 23. (c) 24. (c) 25. (a) 26. (a) 27.(b) 28. (b) 29. (c) 30. (a) 31.(c) 32. (b) 33.) 34. (c) 35. (d) 36. (b) ‘37. (a) 38. (b) 39.) 40. (d) At. (a) 42. (c) 43. (b) 44. (c) 45. (a) 46. (c) 47. (c) 48. (a) 49. (d) 50. (c) 51.(a) 52. (b) 53. (a) 54. (b) 55. (d) 56. (c) 5.10 cy Explanations 1 10. c Ratio & Proportion, Mi WS ena B77 LetA=3x, B= 7x oct Tx=45, x= 45; B=7x= 31.5 iy 1127 Let the fraction be *; x3 yua7s Ifa, b, care in continuous proportion. The mean proportion is b. Therefore, 1c, bP = B x 72, b= 576-24 _2 Ifa, b,c, dareinproportion, 2=—> =! 362135, 2 Third proportional c= 2 = 30=30 as A’ share = P| —* ) = e102 eusa0 me where P = Profit and x, y and z are respective shares of A, B and C. Ratio of their profits = Ratio of their investments = 4000 x 12 : 8000 x 9 : 12000 x 2 48: 72 : 24 2g Saat Bs’ share = 2 x 5200 = €2,600, £-. Letw's share = 2a, 's share = 7a. x's share 2a_2 B's part = 2 ~ 3960-21080 Noshav-— A — aSav3A P=: ure Alligation, Partnership & Average 11. ¢ Letthe number be 5x and 3x. 5x Then, = 60x - 108 = 69x - 207 =9x=99 =x= 11 The first number is 11 * 5 = 56. 12.c B’smoney = 2 800 =1000 C's money = 31000-21800, Therefore, A's + B's + C's money = £3,300. 13.d 4x =3y=22 Divide the three terms by their LCM. LCM of 4, 3,2= 12; Krys 3:4:6 14. c Let the parts be x, (68 — x). 18a > u @IN ain Sb ol> B's share = 2 6900-81200 16.b X's share=3x+30 Y's share > 4x + 20 Z's share— 5x +50 Sum is 9700. 12x + 100 = 9700, 12x = 9600, x= 600. Y's share = 4x + 20 = 3200 + 20 =%3,220. 17. Let Bget®x, Aget®x +70 Cget—80 x+x+70+x-80= 530 > 3x 10 = 530, 3x = 540 =x= 180 A’sshae 180470 280 5 Cssnare Te =4 18.2 Ratio= = Let antecedent = 4x = 36, x= 9. Consequent = 9x = 9x 9= 81 Ratio & Proportion, Mixture Alligation, Partnership & Average 25.a Let man’s age be 7x, son's age = 2x. 19.b 20.b 21.4 2a 2B.c 24.0 A-t,8-20-4-1 B 2 APBEC=12271 Shares of A, B and C are x, 2x and x. Bx a2 x Ratio of coins by value + 3x + 2x + 3x = 600, x Value of 25-paisa coins = 75 x 3 =€225, Number of coins = 225 x 4 = 900. M:W=2: 1. Total volume = 180L. Milk = 120 L, water = 60 L. Let ‘litres of water is added to make the ratio Ae. so 4 worn 2 2240 = 60+x x= 180L. Mos OF in 100 L mixture. milk = 75 L, water = 25 L. After adding 200 L of water, water = 225 L and ilk = 75 L. Ratio = 4:3. 25 Initially number of boys = 250, number of girls = 250. New batch t of the girls (50 girls) left the class and 25 boys joined in. Number of girls remaining = 200, and number of boys = 250 + 25 = 275. Boys _275_it ‘Gits 200° Original population is 15,000. Population after one year = 2000-7 1500 = 1500 «80016500 Population after two years e800 1650-1850 165014850 Short cut: a 10x11 Change in population = 10-10 -79210 Population after 2 years = 15,000 x 0.99 = 14,850 1% 5.11 4 according to question, 7x18 2 = Fae. Te + 15 = 4x + 30, Present age of father = 35 years. Present age of son = 10 years. Father's age when son was born = 35-10 = 25 years. =5 26.d Let present age of son = x, and present age of father = y. (9-4) 6-4) oD (y=12)=2+12) Gi) From (i) and (i), y-6x +20 y-2x-12= 4x = 32, x= B years, y= 28 years. Ratio of ages = 27.b Let $-2-$ a= 3k, b= 4k, c= 7k asp aks € 28.b Sum =84 Itmust be divisible by the sum of the ratios. Sum of the ratios are 12, 8, 24 and 12. Since, 8 does not divide 84. Hence (b) is the correct option. 29. ¢ 0.35 of x= 0.07 of y. 105, tren 8, 703 B°8 Hence, ratio of iron : copper = 103: 105. 31. ¢ Quantity of milk in 80L mixture =} 80-50. and in 16L mixture =$.16= 101 Quantity of water in 80L mixture = 200-901 and in 16L mixture -3 <16-€ 50-10)-16 56 ; Required ration - ie7:3, ora 33.4 34.6 35.4 36.b 38. b 13x, zine = 7x. Copper = 13 x 25= 325 kg A’s effective investment = 16000 x B's effective investment = Cseffective investment Profit sharing ratio = 96 : 96 : 12i.e.8:8:1 Agets 100 paise, B gets 65 paise and C gets 35 paise. Ce share ~ 560- Sum 200 ‘Sum = %3,200. Let the numbers be 2x and 3x. Ratio oftheir squares = 2-2. Note: Ratio of squares is independent of difference of numbers. L:M:0=5:7:3 Let the labour cost be Sx, material cost = 7x, overheads = 3x. Total cost = 15x Profits = 20% of 15x = 3x xT “xs Material eos Profit tip +0) = 2A=B+C (i) 4B=A+C ‘Subtracting (ji) from (i), 2A-4B = B-A=3A=58 0) 3 2a-8 Dy 3,7, c-2n-B-20-2a-2a ae arec-1:2.2-9:3:7 As share = 2 »11250-7605. Bs share = 2 ett20-15008 A's share — B's share = 750 « 2 = %1500. a1 os Let number of boy: Let number of girls = 5x 39.4 40.4 Aa 42.6 43.b Ratio & Proportion, Mixture Alligation, Partnership & Average Tx + 5x = 72, x=6 Number of boys = 42. Number of girs = 30. 12 more girls should be admitted to make the number equal. Let the numbers be 2x, 3x, and 5x respectively. ‘Sum of their squares = 608 ~ 4x? + 9x? + 25x? 38x? = 608, x2 = 16, x==4. Asthe numbers are positive, the biggest number is 20. M:W=2:5. Total volume = 28 L, 2 Mik = 2.26= 8 L. Water = $.26=20L 2 Lof milk is added and 5 L water is removed. (BEB tues Lets income = 23x B'sincome = 22x. A's expenses = @5y. B's expenses Xs savings = B's saving: ‘Solving (i) and (ii), x = 6000 B's income = 2) 12,000. LetA\s, B's and C's investments be 8x, 7x and 5x respectively. Ass effective investment = (8x)5 + (4x)7 40x + 28x = 68x B's effective investment = 7x x 12 = 84x. C's effective investment = 5x x 12 = 60x. @ i) Bshare= 2 «200 =€10,500. 2-3 Let the price be 5x and 4x 5x —4x= 800, Price of rickshaw = 800 x 4 = 73,200. mee 82 saz 84 A+B gas Short cut: LetA= 5. Then B= 2 Therefore, (40 + 18) : (40+ 4)= 58:44 = 29: 22. Ratio & Proportion, Mixture Alligation, Partnership & Average 45. a 20% solution of sugar means one-fifth of suger. In 5 Lof solution, 4 Lis sugar and 4 Lis water. After adding 1 L of water, Percentage of sugar = 4x 100 = 16.67%. 46. c Letthe original consumption be 1 unit costing 100. New cost =%125. New consumption = (4 4 zg” 00) -£ unit. ea Reduction in consumotion grie 1:5, Original consumption 47. c Sum of present ages of all the three =25%2+3+3+1=57 years 48, a Runs scored in first 20 overs = 20x 4.2 = 84 Runs to be scored to reach the target = 312-84 = 228 Required run rate 49. d Sum of ages of Aand B= 60 x 2=120 Cand D=38x2=76 EandF=10x2=20 A+B+C+D+E+F= 120+76+20=216 Hence, the average age of the famih 36 years. 50. c Total sales for 5 days = (6135 + 7227 + 6755 + 7430 + 6462) = 234009. Required sales on the sixth day = [(6600 x 6) — 34009] = &(39600 - 34009) =35591 51. a Average of 50 numbers =| ‘Sum of 0 numbers (0 * 50) = 0. Itis quite possible that atmost 49 of these numbers can be positive and if their sum is ‘e’ then 50th number will be (-a), making the sum total of 50 numbers zero. 5.13 52.b Increase in weight due to replacement of the person weighing 56 kg by a new person =2x10=20kg The weight of the new person = (56 + 20) kg = 76 kg. 53. a Letthe monthly incomes of Ram, Rahim and Salim are x’, '¥ and ‘2’ respectively, then x+y = (4500 x 2) = 9000 “ y += (6500 x 2) = 11000 (i) x+Z= (6100 x 2)= 10200 veil) Adding (i), i) and (il), we get; 2(x + y +z) = 30200 orx+y+z = 15100 -(W) Subtracting (i) from (iv), we get x = 4100. .. Ram's monthly income = %4,100. 54. Since the month begins with a Sunday, so there will be five Sundaysin the month. Requiredaverage 7205 + 450 <25 _ 3600+ 11250 =e oe 85. d Runs made in first 20 overs = 24 * 4.5= 108 Total run to be scored = 50 * 6 = 300 Runs needed to be scored = 300 - 108 = 192. 56. ¢ Let the number of students in the class = x Increase in the total marks = 03x 3x = (63-38) ee 03 Alternative method: =* 150 Total number of students = #2ease in marks

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