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SOE COMPETITIVE CLASSES, , Mixture - Level - 3, , Exercise - 1, , , , Two vessels A and B contain mixtures of spirit and water a, mixture of 3 parts from A and 2 parts from B is found to contain, 29% of spirit and a mixture of 1 profit from A and 9 parts from, Bis found to contain 34% of spirit. find the percentage of spirit, in Band A., , @ ade Aven Ba feve cen ort were) AW 3 AMT Ge BY 2, ant & a fart 4 29% foe F cen AW 1 ATT sik BY 9 ATT, Bat Pert 4 34% fue 21 fre aH fea sat we! (Bae, Aa), , (a) 35,25 (b) 40,20 (c) 25,25 (d) 50, 50, , In a 50 litre mixture of water and milk, water is only 20%. The, milkman gives 10 litres ‘of this’ mixture to a customer and then, he adds up 10 litres of pure water in the remaining mixture. The, percentage of water in the final mixture is :, , uri aie gu & Soe. fret 4, art 20% 81 quae sa Pert, 10 ch. oF WH Tew ot ar z aie gad a ae sy fe A, 10 oh. Yq orf froma & oRomA Perr Yor or oferert fara, al, , (a) 84% — (b) 74% == (c) 26% = (d) 36%, , Peter has a container filled completely with 80% milk and 20%, water. 5 litres of the solution is removed and replaced with, water. Then, 15 litre of this solution is removed and replaced, with water. The milk percentage is now 55%. Which of the, following can be the capacity to the container (in litres)?, , fier G Ue WH UA 80% GT FT 20% UH S YT GIS aT eI, 5 chex facras Prova ur aon Grea @ aa 15 cee facet, Prorcrex, ort S agen Grea S| sta GT 55% F| fT AA oa, a oar ater eri?, , (a) 20 (b) 60 (o) 50 (d) 80, , A milkman purchases 10 litres of milk at Rs. 7 per litre and, forms a mixture by adding freely available water which, constitutes 16.66% of the mixture. Later on he replaced the, mixture by some freely available water and thus the ratio of, milk is to water is 2: 1. He then sold the new mixture at cost, price of milk and replaced amount of mixture at twice the cost, of the milk then what is the profit percentage?, , WH qa 10 chex Ga 7 W/ltr HI ae Y Gia 8 wa AIT A, fier aren urh, ge 4 frerae va fer arate it fe Parr, BT 16.66% | ae H ae |S fra oT qua 4 fer ae or, aaa @ Ud SA TOR BT a UM OT aa 2:18 81 ae, fer ar gud HA W oa ea S| Te seer Ey Pew GT ATaT, a gd wy b erp 4 cam aa ar vfeerad erm?, , (a) 68% — (b) 75% = (c) 60% ~=—(d) 45%, , An empty container is filled with pure alcohol. The alcohol is, slowly allowed to run out and when the container is 1/4 empty., It is replaced with water. Next when the container is half empty, is again filled with water. Finally, when it is 3/4 empty, it is, again filled with water. What percentage of container is alcohol, , now?, , we tet ais oF veoteia S Wt axe ae fear ora e) ada A, , , , 10., , , , fear ore &| fox wa & stem wre eta @, at wert fe yt aE, Burt B a fee ore @| sit Fa Be 3/4 Teh ete z, a, saor fox qt age ort & ay fear ona e1 ade 4 ge war, Veareta #1 Arar eer erie, , 3 11, (a)10% ~—(b) 250 © 0% (9%, , There are two vessels of equal capacity, one full of milk, and the, second one-third full of water. The second sel is then filled up, out of the first, the contents of second are then poured back into, the first till it is full and then again the contents of the first are, poured back into the second till it is full. What is the proportion, of milk in the second vessel?, , 20 20 3 37. 27, or Or Or On, There are two containers A & B of equal volume that contain a, mixture of milk and water in the ratios of 1: 2 and 1: 3, respectively. half the volume of container A is powered into, containing B, and then exactly half the volume of the mixture, from container B is poured into container A calculate the ratio, of milk and water in container A now., Adie Bd war samt & ada & fer ge sie ort oT Perr, war: 1:2 31:3 ¢ ada A oT omen ores ada BA User, ara @ afk fix faega ada B & fem or ater amacd ada A, 4 ren orean @ oh ara ads A H gu site ort ar aqua aarsit 2, (a)3:7 (b) 3:5 (3:8 (7:3, The percentage of alcohol in two wine tanks is 20 and 40, respectively and rest is grape juice. If a wine glass is filled to its, half by the tank 1 and 2 in the ratio 2 : 3 and the rest is filled, again by pure alcohol, then what is ratio of the grape juice to, alcohol in the wine glass ?, a aed & tH F sia 20% six 40% ena 2 BY ah AW z,, sm && 1 sik 2 & srgqura 4 we era ar froma 2:3 site ve, of fox 8 Ye were G ay fear ran @, a aera a roe F si, @ WH OT wa U aad FM es?, (a)17:16 (b) 16:33 (c) 17:50 (d) 17:33, From a solution that has milk and water in the ratio 5 : 3, 'X’, percent is removed and replaced with water. The concentration, of milk in the resulting solution lies between 30% and 50%., Which of the following best describes the value of 'X'?, we fier foert ge go orf or aqua 5s: 3 1 frei @ x’, ferret fart Proven cre & cer or S seer fear Gran 8 | afer, fasror & ger at arat 30% B 50% & aa et om S| 'X' OT AM, SH tel caer 21, (a) 25<x<50 (b) 20<x<52, (0) 20<x<48 (@) 25<x<60, There are two vessels of equal capacity, one full of milk and the, second one third full of water. The second vessel is then filled, up out of the first, he contents of the second are then poured, back into the first fil it is full and there again the content of first, are poured back in to the second till it is full. What is the, proportion of milk in the second vessel., , , , BY-AMRIT SIR

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Answer Key, 1 é 2 d 3 b 4 a 5 b, 6 |b a|sf[a]o9{bifio0{b, ai [c [1z]a/13]ali4]/b/15/ a, 16 | c [17] b] 18] c][ 19] al 20] b, 21 | a |22/c | 23] d/ 24] c | 25] b, an ), Let cone. of spirit in vessel A =x%, and conc of spirit in vessel B = y%, x y, 3x 42x, 100 “100 _ 29°, 5 100, 3x + 2y = 145 . nw (i), 1x 49x, 100 "100 _ 34, 10 100, X + 9y = 340. sew (ii), from (i) and (ii), y=35&x=25, 2 (@, Initial quantity = 50L, Ratio of Milk: Water = 80 :20=4:1, replaced quantity = 10L, 44, ik 50%E- p10, Water soy 2 okt, 5S, = 200-40, 50+40, = 160_16, 90 9, So, water percentage in final mixture = = «100% = 36%, Alternatively:, Total quantity of mixture = 50 litre, . 401 101, Initial (80%) (20%), mixture, (81) (-21) | 10 litre of mixt, is drawn out, Remaining { 321 al, mixture, 10 litres of wat, C10) in mixed, Final 321 181, mixture] (64%) (36%), , See the chart for solution., , , , Initially there is 40 litre (80%) milk in the 50 litres mixture., , , , , , 3, , When 10 litres of mixture is drawn out, it means 8 litres of milk, is drawn out. Now when the 10 litres of water is added. It means, in the 50 litres of mixture, there is only 32 litres of milk, ie.,, , 64%. Hence the percentage of water is 36%., Alternatively:, , When 10 Itr. Is taken out from the mixture the remaining, , mixture is 40 Itr. contains 20% water., And we are adding 100% water 10 Itr. quantity., , 00 NY 20, to BERS, , 16 1:4 64, , Required % = 20 + 16 = 36%, , Or 100 - 64 = 36%, , (@), , Capacity of container = x, , Initial quantity of milk = 0.8x, , 16, 08x (1-2\2-4)- 0.58x > er -5)(X-15) = u, , 1, , 40, , x, 16 (x? - 20x +75) = 11x°=>5x?- 320x +1200 = 0, x2 - 64x + 240 = 0 = (x- 60) (x- 4) =0 > x =60 ltr, @, , 1—> Water, 16.66% = = ., 6 Total mixture, , Milk = 5 unit = 10L., So, water = Lunit = 2L, , Milk 2 water, initial 10 a 2, final 10 a 5, , Total mixture = 15unit = 12L, , Quantity of mixture replaced with water = 3 unit = 2.4L, According to question, CP of milk = 10 x 7= 70, , 12 Itr sold @7 Rs/kg total price = 84 Rs., , 2.4 Itr sold @ 14 Rs/kg Total price = 33.6 Rs, (64+33.6)-70, , Profit 9 = S*°5.9-70 - 68%, , Alternatively:, , 104% = x= x = 2 Itr; SP of mixture = 12 x 7 =84 Rs., 6, , Milk: water 10 :2=5:1, , i 775, , _ 6 2 Ss 15y=365y=24, y, , oe, ew, , SP of new mixture = 2.4 x 14 = 33.6 Rs, Total SP = 84 + 33.6 = 117.6, cP=10x7=70, , Profit = 217-670 x 100 = 68%, 70, , , , @)

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atfirststep 4 : 3 = 1partrunout, , 20d step 2:1, 3rd step 4:1, , 32: 3, , 75 3, Now alcohal 35 x 100 = 3 8”, @), M W M W, 81 0 0 27, 27 0 54 27, 27 +36 18 54-36 72-18, 63 18 18 Q, 43-42 18-12 18 +42 9+ 12, 21 60 60 a, 7 4 Z mo ff 7, 20, , Required ratio = [>, # 27, , (@), , The two containers are of equal volume and contains same, amount of mixture., , Assume the volume of mixtures be 12 litres, , , , , , , , Then, Milk Water, Container A 4 litres 8 litres, Container B 3 litres 9 litres, , , , , , , , , , , , New after first operation, , In container A, , Milk = 2 litres, water = 4 litres and in container B, Milk = 5 litres and water = 13 litres, , After 2% operation, , , , Container A, Milk = 4.5 litres and water = 10.5 litres, Container B, Milk = 2.5 litres and water = 6.5 litres, 453, « Required ratio = ==, a 105 7, @, Alcohol Grape Juice Alcohol: Grape, Tank1 20% 80% 1:4, Tank 2 40% 60% arg, The ratio of grape juice to alcohol in half filled wine, 4 3, 2xs43x>, Glass = 3} at, dxtyaxe 8, , So, the half capacity of the glass = 17 + 8 = 25, , So, full capacity = 25 x 2 = 50, , Now rest 25 parts has to be filled with alcohol., , So the ratio of the grape juice to alcohol, , = 17: (8+25) = 17 : 33., , Alternatively:, , As the wine glass is filled to half by taking two parts from tank, , Land three parts from tank 2 and the second half is equivalent, , to five parts which is pure alcohol, the percentage concentration, , of grape juice is:, , 2x80+3x60+5x0, 24+34+5, , = 34%, , , , , , 9. (b), two cases take between 30% to 50% as milk quantity, (i) for maximum change 30%, , mi: w, 5 of 3, dx, , (5: 3)x3 315:9 y96, (3: 7) x5 3:15:35, , 26, initial = 24 + 26 =50>x%= 7 x 100= 52%, , 50, (ii) for maximum change 50% milk, m:w, 5:3, Lex, 523, , d+x ]4+2, 528, , initial = 8 + 2 = 10 unit >% change =, , , , = 20%, , 10, , xvaries from 20 <x < 52, answer could be marked by only first condition, 10. (b), , , , (31), M:W, Initial 0:1, Istransfer 2:1, Ile transfer 24, 33, Ill transfer 2h FL a 28, 3 °° 9) \3"°"9) 99, 20, Required proportion = 55, , 11. (0), through the whole process no extra diesel is added, so initially 50% diesel, 50% diesel, 425%, , 37.5% Left (3/8), , 1. 3, 4-2/3 (left Sof =), , 1,3 5b s125%, 3.8 8, , 12. (a), After first integration,, Quantity of water = 23 Itr, Quantity of milk = 23 x 4 = 92, After sec. iteration