ALLIGATION AND MIXTURE

Transcription

1 ABOUT DISHA PUBLICATION One of the leading publishers in India, Disha Publication provides books and study materials for schools and various competitive exams being continuously held across the country. Disha's sole purpose is to encourage a student to get the best out of preparation. Disha Publication offers an online bookstore to help students buy exam books online with ease. We, at Disha provide a wide array of Bank / Engg./ Medical & Other Competitive Exam books to help all those aspirants who wish to crack their respective different levels of Bank / Engg./ Medical & Other Competitive exams. At Disha Publication, we strive to bring out the best guidebooks that students would find to be the most useful for all kind of competitive exam. ALLIGATION AND MIXTURE. One litre of water was mixed to litres of sugar. Solution containing % of sugar. What is the percentage of sugar in the solution? (a) (b) (c) (d) Insuffficient data (e) None of these. A trader mixes 80 kg of tea at ` per kg with 0 kg of tea at cost price of ` 0 per kg. In order to earn a profit of %, what should be the sale price of the mixed tea? (a) `. (b) ` (c) ` 0 (d) ` 9.0 (e) None of these. Alcohol cost `.0 per litre and kerosene oil cost `.0 per litre. In what proportion these should be mixed so that the resulting mixture may be `. per litre? (a) : (b) : (c) : (d) : (e) None of these. Pure milk costs `.0 per litre. A milkman adds water to litres of pure milk and sells the mixture at ` per litre. How many litres of water does he add? (a) litres (b) litres (c) litres (d) litres (e) None of these. In what ratio must water be mixed with milk to gain 0% by selling the mixture at cost price? (a) : (b) : (c) : (d) : 0 (e) None of these. A chemist has 0 litres of a solution that is 0 per cent nitric acid by volume. He wants to dilute the solution to per cent strength by adding water. How many litres of water must he add? (a) (b) 0 (c) 8 (d) (e) None of these. In what ratio must water be mixed with milk to gain % on selling the mixture at cost price? (a) : (b) : (c) : (d) : (e) None of these 8. An alloy contains copper and zinc in the ratio : and another alloy contains copper and tin in the ratio 8 :. If equal weights of both the alloys are melted together, then the weight of tin in the resulting alloy per kg will be: (a) (d) 0 (b) (e) None of these 9. The ratio of milk and water in litres of adulterated milk is :. How much water must be added to make the mixture s ratio :? (a) lt (b) 0 lt (c) lt (d) lt (e) None of these 0. A and B are two alloys of gold and copper prepared by mixing metals in the ratio : and : respectively. If equal quantities of the alloys are melted to form a third alloy C, then the ratio of gold and copper in alloy C will be (a) : (b) : 9 (c) : (d) 9 : (e) None of these. Sameer bought 0 kg of tea at ` per kg and 8 kg at ` 0 per kg. He mixed both the brands and sold it at a total profit of `. What was the selling price per kg of the mixture? (a) ` 8 (b) ` 0 (c) ` 9 (d) ` (e) None of these (c) 0 RESPONSE GRID. a b c d e. a b c d e. a b c d e. a b c d e. a b c d e. a b c d e. a b c d e 8. a b c d e 9. a b c d e 0. a b c d e. a b c d e. a b c d e

2 . How many litres of pure alcohol must be added to 0 litres of mixture which is % alcohol to make a mixture which will be % alcohol? (a) (d) (b) (e) None of these. How many kg of custard powder costing ` 0 kg must be mixed with kg of custard powder costing ` kg so that % may be gained by selling the mixture at ` 0 kg? (a) kg (b) kg (c) kg (d) 0 kg (e) None of these. 00 gm of sugar solution has 0% sugar in it. How much sugar should be added to make it 0% in the solution? (a) 0 gm (b) 0 gm (c) 0 gm (d) 0 gm (e) None of these. Gold is 9 times as heavy as water and copper 9 times. In what ratio should these metals be mixed so that the mixture may be times as beavy as water? (a) : (b) : (c) : (d) : (e) None of these. In a mixture of 0 litres, the ratio of milk to water is :. If the ratio of milk to water is to be :, then amount of water to be further added is. (a) 0 (b) 0 (c) 0 (d) 80 (e) None of these. In a mixture of milk and water the proportion of water by weight was %. If in 0 gm of mixture gm water was added, what would be the percentage of water? (Weight in gm) (a) % (b) 88% (c) 90% (d) 00% (e) None of these 8. In what ratio must tea at Rs. per kg be mixed with tea at Rs. per kg so that the mixture must be worth Rs..0 per kg? (a) : (b) : (c) : (d) : (e) None of these (c) 9. Two vessels A and B contain spirit and water mixed in the ratio : and : respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8 :? (a) : (b) : (c) : (d) : 9 (e) None of these 0. If 0% of a : solution of milk and water is replaced with water, then the concentration of the solution is reduced by: (a) % (b).% (c) 0% (d) % (e) None of these. In a mixture of litres, the ratio of milk and water is :. How much water must be added to make the ratio 9 :? (a) 0 litres (b) litres (c) litres (d) 0 litres (e) None of these. Three containers A, B and C are having mixtures of milk and water in the ratio :, : and :, respectively. If the capacities of the containers are in the ratio : :, then find the ratio of the milk to the water if the mixtures of all the three containers are mixed together. (a) : (b) : (c) : (d) : (e) None of these. Five litres of water is added to a certain quantity of pure milk costing Rs. per litre. If by selling the mixture at the same price as before, a profit of 0% is made, then what is the amount of pure milk in the mixture? (a) 0 litres (b) 0 litres (c) litres (d) litres (e) None of these. How many kg of tea worth Rs per kg must be blended with 0 kg of tea worth Rs 0 per kg so that by selling the blended variety at Rs 0 per kg there should be a gain of 0%? (a) kg (b) 0 kg (c) kg (d) kg (e) None of these. How many kg of sugar costing Rs. per kg should be mixed with kg of cheaper sugar costing Rs.0 per kg so that the mixture is worth Rs.0 per kg? (a) 0 kg (b) 00 kg (c) 0 kg (d) kg (e) None of these RESPONSE GRID. a b c d e. a b c d e. a b c d e. a b c d e. a b c d e 8. a b c d e 9. a b c d e 0. a b c d e. a b c d e. a b c d e. a b c d e. a b c d e. a b c d e

3 HINTS & SOLUTIONS. (a) New % of sugar in ( + ) litre solution % ( + ) (c) C.P. of mixture ` (00 + ) \ S.P. `0 00. (b) By the rule of alligation, we have Cost of Alcohol Cost of Kerosene Oil Rs.0 ` cost of mixture `. 0. \ Required ratio i.e.: 0.. (b) In mixture, Quantity of pure milk - 0 Quantity of water Since in every litres of milk, he adds litre of water. \ In every litres of milk, he adds litres of water.. (b) Let C.P. of milk be Re. per litre. Then, S.P. of litre of mixture Re.. Gain 0% æ00 ö \ C.P. of litre of mixture ` ç `. è0 ø C.P. of litre of water 0 Re. Mean price Re. C.P. of litre of milk 0 \ Ratio of water and milk : :.. (a) Out of 0 litre of solution, there is litres of nitric acid and 9 litres of water. Let x litres of water be added to the solution so that the diluted solution is of % strength. \ % of (0 + x) Þ x.. (a) Let C.P. of litre milk be Re.. S.P. of litre of mixture Re., Gain 0 %. \ C.P. of litre of mixture Re.. C.P. of litre of water 0 Re. Mean price Re. C.P. of litre of milk \ Ratio of water and milk : :. 8. (b) The first alloy does not have tin. Therefore, quantity of tin in units of the resulting alloy Þ Quantity of tin in one unit of the resulting alloy 9. (b) By the rule of alligation, water concentration, Original solution (mixture) Water \ water must be added to the mixture in the ratio : i.e. : Quantity of water to be added 0 litres

4 0. (c) Gold Copper Type A Type B Type C \ The ratio of the Gold and Copper in the type C alloy :.. (c) C. P. of mixture of 8 kg ` 80 \ S. P. C. P. + Profit 80 + ` 88 \ S. P. ` 88 for 8 kg \ S. P. for kg.. (d) By the rule of alligation, Alcohol concentration : Original mixture % 88 Rs ` 9 8 Pure alcohol 00%. (c) Apply the alligation on fracfion of milk in each mixture. Mixture Water 0 Ratio of mixture to water : Therefore, if there is 0 liture of solution, 0 litres of water should be added.. (e) Initially water (weight) gm & milk gm. After added gm water the percentage of water weight of water total weight of mixture % 8. (a) By the rule of alligation: Cost of kg tea of st kind % % 0% \ Alcohol must be added in the ratio of 0 : or : \ Quantity of alcohol to be added in 0 litres (b) C. P. of mixture ` 8 (00 + ) Let x kg be mixed. Then, 0 x x Þ 8x [-8] Þ x kg. (c) The existing solution has 0% sugar. And sugar is to be mixed; so the other solution has 00% sugar. So, by alligation method:. (b) 0% 00% 0% 0% 0% \ The two mixtures should be added in the ratio :. Therefore, required sugar 00 0 gm Gold Copper 9 9 \ Gold : Copper : : \ Required ratio 0 : 0 :. 9. (d) Let the C.P. of spirit be Re. per litre. Spirit in litre mix. of A litre; C.p. of a litre mix. in A Re.. Spirit in litre mix. of B litre; C.P. of litre mix. in B Re.. 8 Spirit in litre mix. of C litre; Mean price Re. 8. C.P. of litre mixture in A C.P. of litre mixture in B æ ö æ ö è ø Mean price è ø æ 8 ö è ø æ ö 9 è ø 9 \ 9 Required ratio : : (c) Let the quantity of milk and water be 0 litres and 0 litres, respectively. (Q Ratio of milk to water : ) After removing 0% of solution Quantity of milk 0 litres and Quantity of water 0 litres Therefore, the concentration of the solution is reduced from 0 to 0 i.e. a reduction of 0%.

5 . (b) Quantity of milk litres Quantity of water 8litres Let x litres of water be added to make the ratio 9 :. 8 + x \ Þ 8 + x Þ x l 9. (c) Ratio of milk in the containers are, : : : : 8 and the ratio of water in the containers are, : : : : 8 Ratio of mixture of milk and water in the containers æ ö æ ö ç + + : ç + + è 8 ø è 8 ø 0 : 0 :. (c) Let the quantity of pure milk be x litres. If litres of water is added to it, then the cost of ( + x) litres Rs. x S.P. of ( + x) litres Rs. (x + ) \ Profit Rs. Given 0% of x x Þ Þ x \ The amount of pure milk in the mixture is litre. (c) Let the weight of tea worth Rs per kg x kg. According to question éx + 0 0ù \ 0% of ê 0 x + 0 ú ë û Þ 0 é x ù 0 00 ê x + 0 ú ë û Þ (x + 900) 00 (x+0) Þ x x or x 900 \ x kg.. (b) Let, weight of sugar costing Rs. per kg x kg x (x + ) Þ.x +.0.0x +.0 Þ 0.x \ x 00 kg