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📁 aptitude book by r s aggarwal
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<html><table height="500" width="1000" border="2"><TR height="5" width="1000"><strong><center><marquee><font color="Green"><h1>APTITUDE</h1></center></strong></font></TR></marquee><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="pnumbers.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="clocks.html" ><b>BACK</b></a><h2 align="center"><b>CLOCKS</b></h2><br><br><font size="4">Medium Problems<br><br><br><u>Type3  </u>:  At what time between 4 and 5 o'clock will the hands of a clock be at <br> rightangle?<br><br>Solution  : In this type of problems the formulae is<br>                                (5*x + or -15)*(12/11)<br> 	Here x is replaced by the first interval of given time here i.e 4<br><br>     Case 1 :       (5*x + 15)*(12/11)<br>		     (5*4 +15)*(12/11)<br>                     (20+15)*(12/11)<br>		      35*12/11=420/11=38 2/11 min.<br>              Therefore they are right angles at 38  2/11 min .past4 <br><br>    Case 2  :      (5*x-15)*(12/11)<br>		   (5*4-15)*(12/11)<br>		   (20-15)*(12/11)<br>                   5*12/11=60/11 min=5  5/11min<br>            Therefore they are right angles at 5  5/11 min.past4.<br><br> <u>Another shortcut for type 3 is</u>   :Here the given angle is right angle i.e 900.<br><br>      Case 1 : The formulae is  6*x-(hrs*60+x)/2=Given angle<br>					6*x-(4*60+x)/2=90<br>					6*x-(240+x)/2=90<br>					12x-240-x=180<br>					11x=180+240<br>					11x=420<br>					     x=420/11= 38  2/11 min<br><br>		Therefore they are at right  angles at 38  2/11 min. past4.<br><br>      Case 2 : The formulae is (hrs*60+x)/2-(6*x)=Given angle<br>                                     (4*60+x)/2-(6*x)=90<br>			              (240+x)/2-(6*x)=90<br>				      240+x-12x=180<br>           				-11x+240=180<br>					240-180=11x	<br>			                                	x=60/11= 5  5/11 min<br><br>			Therefore they art right angles at 5  5/11 min past4.<br><br><u>Type 4 </u> : Find at what time between 8 and 9 o'clock will the hands of a clock be<br><br> in the same straight line but not together ?<br>Solution  : In this type of problems the formulae is<br><br>                                                                     (5*x-30)*12/11<br>             x is replaced by the first interval of given time Here i.e 8    <br>                                     (5*8-30)*12/11<br>				     (40-30)*12/11<br>			             10*12/11=120/11 min=10 10/11 min.<br>                       Therefore the hands will be in the same straight line but not<br> together at 10  10/11 min.past 8.<br><br><u>Another shortcut for type 4 is</u>   : Here the hands of a clock be in the same<br> straight line but not together the angle is 180 degrees.<br>                   The formulae is (hrs*60+x)/2-(6*x)=Given angle<br>        				(8*60+x)/2-6*x=180<br>					(480+x)/2-(6*x)=180<br>					480+x-12*x=360<br>					11x=480-360<br>					x=120/11=10  10/11 min.<br>                   therefore the hands will be in the same straight line but not<br> together at 10  10/11 min. past8.<br><u>Type 5 </u> :  At what time between 5 and 6 o鈥
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