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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" target="right"><strong>Decimal Fractions</strong></a></TR><br><TR><a href="simplification.html"><strong>Simplification</strong></a></TR><br><TR><a href="squareandcuberoot.html" target="right"><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" target="right"><strong>Percentage</strong></a></TR><br><TR><a href="profitandloss.html" target="right"><strong>Profit and Loss</strong></a></TR><br><TR><a href="ratioandproportion.html" target="right"><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" target="right"><strong>Time and Work</strong></a></TR><br><TR><a href="pipesandcisterns.html" target="right"><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" target="right"><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" target="right"><strong>Simple Interest</strong></a></TR><br><TR><a href="CI.html" target="right"><strong>Compound Interest</strong></a></TR><br><TR><a href=""><strong>Logorithms</strong></a></TR><br><TR><a href="areas.html" target="right"><strong>Areas</strong></a></TR><br><TR><a href="volume.html" target="right"><strong>Volume and Surface area</strong></a></TR><br><TR><a href="races.html" target="right"><strong>Races and Games of Skill</strong></a></TR><br><TR><a href="calendar.html" target="right"><strong>Calendar</strong></a></TR><br><TR><a href="clocks.html" target="right"><strong>Clocks</strong></a></TR><br><TR><a href="" target="right"><strong>Stocks ans Shares</strong></a></TR><br><TR><a href="true.html" target="right"><strong>True Discount</strong></a></TR><br><TR><a href="banker1.html" target="right"><strong>Bankers Discount</strong></a></TR><br><TR><a href="oddseries.html" target="right"><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" target="right" ><strong>Permutations and Combinations</strong></a></TR><br><TR><a href="pinkivijji_puzzles.html" target="right"><strong>Puzzles</strong></a></TR></table></TD><TD ><a href="races.html"><b>BACK</b></a><font size=5 ><div align="center">RACES AND GAMES OF SKILL<div align="center"></div></div></font><font><br><br><font size="4"><B>PROBLEMS</B> :-1) In a 1 km race,A beats B by 28 m or 7sec.Find A's time over the course?Sol: B covers 28 m in 7sec     so,B's time over the course = 7/28 *1000 =250 sec        A's time over the course =250-7                                  =243 sec                                 = 4min ,3 sec.<br><br>2) A runs 1 3/4 times as fast as B.If A gives B a start of 84 m,how far must    be winning post be so that A and B might reach it at the same time ?  Sol: Ratio of rates of A:B =7/4 :1                             =7 :4                     In a game of 7 m A gains 3m over B.                      3m are gained by A in a race of 7m                      84 m are gained by A in a race of 7*84/3 =196 m       Winning post must be 196m away from the starting point.<br><br>3)A can run 1km in 3 min ,10sec and B can cover same distance in 3 min 20 sec.  By what distance A beat B?    Sol: clearly A beats B by 10 sec.         Distance covered by B in 10 sec =1000/200 *10                                          =50 m              A beats B by 50 metres.<br><br>4) In a 100m race,A runs at 8km per hour.If A gives b a    start of 4 m and still beats him by 15 sec,what is the   speed of B?Sol: 8000 m -------60*60 sec     100m  ------- 60*60*1000/8000                    =45 sec.Time taken by A to cover 100m =45 sec.     B covers 100-4 m =96 min 45 sec                      =60 sec       B's speed =96 *60*60/60*1000               =5.76 km/hr<br><br>5) A and B take part in 100m race .A runs at 5km per hour.   A gives B a start of 8 m and still beats him by 8 sec.   What is the speed of B?  Sol : A'speed = 5km/hr                =5*5/18                =25/18 m/s        Time taken by A to cover 100m =100*18/25                                      =7.2 sec        Time taken by A to cover 92m  = 72+8                                      =80 sec               B's speed =92*18/80*5                         = 4.14 kmph.<br><br>6) A runs 1 2/3 times as fast as B.If A gives B a start of 80 m,   how far must the winning post be so that A and B might reach    if at the same time? Sol: Ratio of the speed of A and B =5/3 :1      Thus  in a race of 5m ,A gains 2m over B             2m are gained by in a race of 5m             80 m will be gained by A in a race of 5/2* 80                                               =200 m<br><br>7)  A,B and C are three contestans in a kmrace .If A can give B a     start of 40 m and A can give C a start of 64 m,how amny metres    start can b give C? Sol: A covers  100m,B covers (1000-40) =960 m      C covers 1000-64 m or 936mwhen B covers 960 m,C covers 936 mwhen B covers 1000 m,C covers 936*1000/960 m =975 m     B can give C a start of 1000-975 or 25 m.<br><br>8) In a 100m race,A covers the distance in 36 sec and B in 45 sec.In    this race A beats B by?Sol: Distance covered by B in 9secs =100*9/45                                    =20 m     A beats B by 20m<br><br>9) In a 200 m race A beats B by 35m or 7 sec.What is the A's time over    the course?   Sol: B runs 35 m in 7sec.        B covers 200m in =7*200/35                         = 40 sec.        B's time over the course =40 sec        A's time over the course =40-7                                 =33 sec.<br><br>10) In a 300 m race A beats B by 22.5 m or 6 sec.What is the B's     time over the course?    Sol:        B runs 22.5 m in 6sec.        B runs 300m in =6*300*2/45                       =80 sec.        B's time over the course =80 sec.<br><br>11) A can run 22.5 m while B runs 25 m.In a kilometre race B beats A by?    Sol: B runs 25 m ,A runs 45/2 m         B runs 1000 A runs = 1000*45/2*25                            =900m         B beats A by 100m<br><br>12)In a 500 m race, the ratio of the speeds of two contestants A and B is    3:4.A has a start of 140 m.Then ,A win by B? Sol: The speeds of A and B =3:4      To reach the winning post A will have to cover a distance of 500-140 m       i.e 360 m while A covers 3m ,b covers 4m            A covers 360m B covers 4/3*360=480m      Thus when A reaches the winning post, b covers 480m and therefore remains      20m behind.             A wins by 20m.<br><br>13) In a 100m race,A can beat B by 25 m and B can beat c by 4m.In the same race     A can beat C by/   Sol: If A:B =100 :75           B :C=100 :96           then            A :C =A/B*B/C=100/75* 100/96                = 100/72        A beats C by 100 -72 m=28 m<br><br>14) In a 100 race,A can give B 10 mand C 28 m.In the same race B can give C?    Sol: A:B =100 :90         A :C=100 :72         B:C =B/A *A/C             =90/100*100/72             =90/72         When B runs 90 C runs 72         when B runs 100 C runs =72*100/90              B beats C by 20m<br><br>15) In a 100m race ,A beats B by 10 m and C by 13 m.In the race of 180m.    B will beat c by?   Sol :A : B =100 :90     A/B =100/90     A/C =100/87     B/C =B/A *A/C          =90 /87   When B runs 90m C runs 87   When B runs 180 m then C runs =87 *180/90     B beats C by 180-174= 6m<br><br>16) In a race of 200 m, A can beat B by 31 m and C by 18m.In arace of 350 m,    C will beat B by? Sol : In a race of 200 m         A :B =200:169         A :C =200 :182         C/B =C/A*A/B             =182/200*200/169       When C runs 182 m B runs 169       when C runs 350 m B runs =350*169/182                                =325m<br><br>17) In agame of 100 points A can give B 20 points and C 28 points then B     can give C?     In a game of 100 points.        A :B =100 :80        A :C =100 :72         B/C=B/A*A/C            =80/100*100/72            = 80/72      when B runs 80m C runs 72      when B runs 100m C runs =100*72/80                              =90      B can give C 10 points in agame of 100.<br><br>18)At a game of billiards,A can give B 15 points in 60 and A can    give C 20 points in60.How amny points can B give C in a game of 90?Sol: A:B =60:45     A:C =60:40      B/C =B/A*A/C          =45/60*60/40          =90/80     B can give C 10 points in agame of 90.<br><br>19) in agame of 80 points,A can give B 5 points and C 15 points.then     how many points B can give C in agame of 60? Sol: A :B =80 :75      A :C =80:65      B/C=B/A*A/C         = 75/80*80/65         =15/13     B:C =60:52<br><br><a href="races.html"><b>BACK</b></a></font></pre></TD></TR></table></html>
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