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<html><table height="500" width="1000" border="2"><TR height="5" width="1000"><strong><center><h2>APTITUDE</h2></center></strong></TR><TR><TD align="left" width="200" valign="top"><table><TR><a href="numbers.html"><strong>Numbers</strong></a></TR><br><TR><a href="hcf.html"><strong>H.C.F and L.C.M</strong></a></TR><br><TR><a href="dec.html"><strong>Decimal Fractions</strong></a></TR><br><TR><a href="simplification.html"><strong>Simplification</strong></a></TR><br><TR><a href="squareandcuberoot.html"><strong>Square and Cube roots</strong></a></TR><br><TR><a href="average.html" ><strong>Average</strong></a></TR><br><TR><a href="numbers.html" ><strong>Problems on Numbers</strong></a></TR><br><TR><a href="problemsonages.html"><strong>Problems on Ages</strong></a></TR><br><TR><a href="surdsandindices.html"><strong>Surds and Indices</strong></a></TR><br><TR><a href="percent.html"><strong>Percentage</strong></a></TR><br><TR><a href="profitandloss.html"><strong>Profit and Loss</strong></a></TR><br><TR><a href="ratioandproportion.html"><strong>Ratio And Proportions</strong></a></TR><br><TR><a href="partnership.html"><strong>Partnership</strong></a></TR><br><TR><a href="chainrule1.html"><strong>Chain Rule</strong></a></TR><br><TR><a href="timeandwork.html"><strong>Time and Work</strong></a></TR><br><TR><a href="pipesandcisterns.html"><strong>Pipes and Cisterns</strong></a></TR><br><TR><a href="timeanddistance.html"><strong>Time and Distance</strong></a></TR><br><TR><a href="trains.html"><strong>Trains</strong></a></TR><br><TR><a href="boats.html"><strong>Boats and Streams</strong></a></TR><br><TR><a href="alligation.html"><strong>Alligation or Mixture </strong></a></TR><br><TR><a href="simple.html"><strong>Simple Interest</strong></a></TR><br><TR><a href="CI.html"><strong>Compound Interest</strong></a></TR><br><TR><a href=""><strong>Logorithms</strong></a></TR><br><TR><a href="areas.html"><strong>Areas</strong></a></TR><br><TR><a href="volume.html"><strong>Volume and Surface area</strong></a></TR><br><TR><a href="races.html"><strong>Races and Games of Skill</strong></a></TR><br><TR><a href="calendar.html"><strong>Calendar</strong></a></TR><br><TR><a href="clocks.html"><strong>Clocks</strong></a></TR><br><TR><a href=""><strong>Stocks ans Shares</strong></a></TR><br><TR><a href="true.html"><strong>True Discount</strong></a></TR><br><TR><a href="banker1.html"><strong>Bankers Discount</strong></a></TR><br><TR><a href="oddseries.html"><strong>Oddmanout and Series</strong></a></TR><br><TR><a href=""><strong>Data Interpretation</strong></a></TR><br><TR><a href="probability.html"><strong>probability</strong></a></TR><br><TR><a href="percom1.html" ><strong>Permutations and Combinations</strong></a></TR><br><TR><a href="pinkivijji_puzzles.html"><strong>Puzzles</strong></a></TR></table></TD><TD valign="top"><a href="alligation.html" name="right"><b>BACK</b></a><font size="5"><center><b>ALLIGATION OR MIXTURES</b></center></font><br><br> <font size="5"><b>SOLVED PROBLEMS</b></font><br><br><br><br> <font size="4"> <b>Complex Problems</b>:<br><br>1.Tea worth Rs 126 per Kg are mixed with a third variety in <br>the ratio 1:1:2. If the mixture is worth Rs 153 per Kg ,<br>the price of the third variety per Kg will be?<br><br>Solution:<br>Since First and second varieties are mixed in equal proportions<br> so their average price =Rs (126+135)/2 = 130.50.<br><br>So the mixture is formed by mixing two varieties ,one at<br> Rs 130.50 per Kg and the other at say Rs x per Kg in the<br> ratio 2:2 i e,1:1 we have to find x.<br><br><pre>Costof 1Kg tea of 1st kind RS 130.50 Costof 1Kg tea of 2n d kind Rs x. Mean Price Rs 153 x-153 22.50</pre><br> (x=153)/22.5 = 1 =>x-153 = 22.5 <br> x = 175.50.<br>Price of the third variety =Rs 175.50 per Kg.<br><br><br>2.The milk and water in two vessels A and B are in the ratio 4:3 <br>and 2:3 respectively. In what ratio the liquids in both the <br>vessels be mixed to obtain a new mixture in vessel c <br>consisting half milk and half water?<br><br>Solution:Let the C.P of milk be Re 1 per liter.<br>Milk in 1 liter mixture of A = 4/7 liter.<br>Milk in 1 liter mixture of B = 2/5 liter.<br>Milk in 1 liter mixture of C = 1/2 liter.<br>C.P of 1 liter mixture in A=Re 4/7<br>C.P of 1 liter mixture in B=Re 2/5.<br>Mean Price = Re 1/2.<br>By rule of allegation we have:<br><br><pre>C.P of 1 liter mixture in A C.P of 1 liter mixture in B 4/7 2/5 Mean Price 陆 1/10 1/14</pre><br>Required ratio = 1/10 : 1/14 = 7:5.<br><br>3.How many Kg s of wheat costing him Rs 1.20,Rs 1.44 <br>and Rs 1.74 per Kg so that the mixture may be worth <br>Rs 1.41 per Kg?<br><br>Solution:<br>Step1:Mix wheat of first and third kind to get a mixture<br> worth Rs 1.41 per Kg.<br><br><pre>C.P of 1 Kg wheat of 1st kind 120p C.P of 1 Kg wheat of 3rd kind 174p Mean Price 141p 33 21</pre><br>They must be mixed in the ratio =33:21 = 11:7<br><br>Step2:Mix wheats of 1st and 2n d kind to obtain a mixture<br> worth of 1.41.per Kg.<br><br><pre>C.P of 1 Kg wheat of 1st kind 120p C.P of 1 Kg wheat of 2n d kind 144p Mean Price 141p 3 21</pre><br>They must be mixed in the ratio = 3:21=1:7.<br><br>Thus,Quantity of 2n d kind of wheat / Quantity of<br> 3rd kind of wheat = 7/1*11/7= 11/1<br>Quantities of wheat of 1st :2n d:3rd = 11:77:7.<br><br><br>4.Two vessels A and B contain spirit and water mixed in <br>the ratio 5:2 and 7:6 respectively. Find the ratio n which<br> these mixture be mixed to obtain a new mixture in vessel <br>c containing spirit and water in the ratio 8:5?<br><br>Solution:Let the C.P of spirit be Re 1 per liter.<br>Spirit in 1 liter mix of A = 5/7 liter.<br>C.P of 1 liter mix in A =5/7.<br>Spirit in 1 liter mix of B = 7/13 liter.<br>C.P of 1 liter mix in B =7/13.<br>Spirit in 1 liter mix of C = 8/13 liter.<br>C.P of 1 liter mix in C =8/13.<br><br><pre>C.P of 1 liter mixture in A 5/7 C.P of 1 liter mixture in B 7/13 Mean Price 8/13 1/13 9/91</pre><br>Therefore required ratio = 1/13 : 9/91 = 7:9.<br><br><br>5.A milk vendor has 2 cans of milk .The first contains 5% water<br> and the rest milk. The second contains 50% water. How much milk<br> should he mix from each of the container so as to get 12 liters<br> of milk such that the ratio of water to milk is 3:5?<br><br>Solution:Let cost of 1 liter milk be Re 1.<br>Milk in 1 liter mixture in 1st can = 3/4 lit.<br>C.P of 1 liter mixture in 1st can =Re 3/4<br>Milk in 1 liter mixture in 2n d can = 1/2 lit.<br>C.P of 1 liter mixture in 2n d can =Re 1/2<br>Milk in 1 liter final mixture = 5/8 lit.<br>Mean Price = Re 5/8.<br><br><pre>C.P of 1 lt mix in 1st Re3/4 C.P of 1 lt mix in 2nd Re1/2 Mean Price 5/8 1/8 1/8</pre><br>There ratio of two mixtures =1/8 :1/8 = 1:1.<br>So,quantity of mixture taken from each can=1/2*12 <br> = 6 liters.<br><br><br>6.One quantity of wheat at Rs 9.30 p<br>er Kg are mixed<br> with another quality at a certain rate in the ratio 8:7. <br>If the mixture so formed be worth Rs 10 per Kg ,what is <br>the rate per Kg of the second quality of wheat? <br> <br> Solution:Let the rate of second quality be Rs x per Kg.<br><br><pre>C.P of 1Kg wheat of 1st 980p C.P of 1 Kg wheat of 2nd 100x p Mean Price 1000p 100x-1000p 70 p</pre><br> (100x-1000) / 70 = 8/7<br> 700x -7000 = 560<br> 700x = 7560 =>x = Rs 10.80.<br>Therefore the rate of second quality is Rs10.80 <br><br><br>7.8lit are drawn from a wine and is then filled with water.<br>This operation is performed three more times.The ratio of<br> the quantity of wine now left in cask to that of the water<br> is 16:81. How much wine did the cask hold originally?<br><br>Solution:<br>Let the quantity of the wine in the cask originally be x liters.<br>Then quantity of wine left in cask after<br> 4 operations = x(1- 8/x)4lit.<br>Therefore x((1-(8/x))4)/x = 16/81.<br> (1- 8/x)4=(2/3) 4<br> (x- 8)/x=2/3<br> 3x-24 =2x<br> x=24.<br><br><br>8.A can contains a mixture of two liquids A and B in the<br> ratio 7:5 when 9 liters of mixture are drawn off and the <br>can is filled with B,the ratio of A and B becomes 7:9. <br>How many liters of liquid A was contained by the can initially?<br><br>Solution:<br>Suppose the can initially contains 7x and 5x liters <br>of mixtures A and B respectively .<br>Quantity of A in mixture left = (7x- (7/12)*9 )lit<br> = 7x - (21/4) liters.<br>Quantity of B in mixture left = 5x - 5/12*9<br> = 5x - (15/4) liters <br><br>Therefore (7x 鈥⌨️ 快捷键说明
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