{"id":6016,"date":"2025-06-09T14:10:24","date_gmt":"2025-06-09T14:10:24","guid":{"rendered":"https:\/\/thecompanyboy.com\/?p=6016"},"modified":"2025-06-09T14:10:24","modified_gmt":"2025-06-09T14:10:24","slug":"rs-aggarwal-quantitative-aptitude-pdf-download-races-games-and","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/drive\/rs-aggarwal-quantitative-aptitude-pdf-download-races-games-and\/","title":{"rendered":"RS Aggarwal Quantitative Aptitude PDF Free Download: RACES AND GAMES"},"content":{"rendered":"

RACES AND GAMES<\/u><\/strong><\/h1>\n

IMPORTANT FACTS<\/u><\/strong><\/h2>\n

\u00a0<\/strong>Races:<\/strong> A contest of speed in running, riding, driving, sailing or rowing is called race<\/p>\n

\u00a0<\/strong>Course:<\/strong> The ground or path on which contests are made is called a race course.<\/p>\n

\u00a0<\/strong>Starting<\/strong> Point:<\/strong> The point from which a race begins is known as a starting point.<\/p>\n

\u00a0<\/strong>Winning Point or Goal:<\/strong> The point set to bound a race is called a winning paint or a goal.<\/p>\n

\u00a0<\/strong>Winner:<\/strong> The person who first reaches the winning point is called a winner.<\/p>\n

\u00a0<\/strong>\u00a0Dead Heat<\/strong> Race:<\/strong> If all the persons contesting a race reach the goal exactly at the same time, then the race is said to be a dead heat race.<\/p>\n

Start:<\/strong> Suppose A and B are two contestants in a race. If before the start of the race, A is at the starting point and B is ahead of A by 12 metres, then we say that ‘A gives\u00a0 B, a start of 12 metres.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ‘<\/p>\n

To cover a race of 100 metres in this case, A will have to cover 100 metres while B\u00a0 will<\/p>\n

have to cover only (100 – 12) = 88 metres.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 i<\/p>\n

In a 100 m race, ‘A can give B 12 m’ or ‘A can give B a start of 12 m’ or ‘A beats\u00a0 12 m’ means that while A runs 100 m, B runs (100 – 12) = 88 m.<\/p>\n

\u00a0<\/strong>Games:<\/strong> ‘A game of 100, means that the person among the contestants who scores 100m first is the winner.<\/p>\n

If A scores 100 points while B scores only 80 points, then we say that ‘A can give B 20 points.<\/p>\n

\u00a0<\/em>\u00a0<\/u><\/strong>SOLVED EXAMPLES :<\/u><\/strong><\/p>\n

Ex. 1. In a km race, <\/em>A beats B by 28 metres or 7 seconds. Find A’s time <\/strong>over <\/strong>the course.<\/strong><\/p>\n

\u00a0<\/strong>Sol.<\/strong>\u00a0 Clearly, B covers 28 m in 7 seconds.<\/p>\n

:. B’s time over the course = (278 <\/u>x 1000) sec = 250 seconds.<\/p>\n

:. A‘s\u00a0 <\/em>time over the course = (250 – 7-) sec = 243 sec = 4 min. 3 sec.<\/p>\n

\u00a0<\/strong>Ex. 2. A\u00a0 runs 1 \u00be \u00a0times as fast as B. if A gives B a start of 84 m, bow far must\u00a0\u00a0\u00a0\u00a0 <\/strong><\/p>\n

winning post be so that A and B might reach it at the same time?<\/strong><\/p>\n

Sol<\/strong>. Ratio of the rates of A and B =\u00a0 7\/4\u00a0 : 1\u00a0\u00a0 = 7 : 4.<\/p>\n

So, in a race of 7 m, A gains 3m over B.<\/p>\n

:. 3 m are gained by A in a race of 7 m.<\/p>\n

:. 84 m are gained by A in a race of (7\/3 x 84) m = 196 m.<\/p>\n

:. Winning post must be 196 m away from the starting point.<\/p>\n

\u00a0<\/strong>Ex. 3. A can run 1 km in 3 min. 10 sec. and B can cover the same distance in\u00a0 3 min. 20 sec. By what<\/strong> distance can A beat <\/strong>B <\/strong>?<\/strong><\/p>\n

\u00a0<\/em>Soln<\/strong>:Clearly, A beats B by 10 sec.<\/p>\n

Distance covered by B in 10 sec. = (1000 <\/u>x 10 )m = 50 m.\u00a0\u00a0\u00a0\u00a0<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 200\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

Therefore\u00a0 A beats B by 50 metres.<\/p>\n

Ex .4 . In <\/strong>a 100 m race, A runs at 8km\u00a0 per hour. If A gives B a start of 4 m and still him by 15 seconds, what is the speed of B ?<\/strong><\/p>\n

Sol: <\/strong>Time taken by A to cover 100 m\u00a0 =(60 X 60 \/ 8000)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x 100 sec = 45 sec.<\/p>\n

B covers (100 – 4) m\u00a0 =\u00a0 96 m\u00a0\u00a0 in\u00a0 (45 + 15) sec = 60 sec.<\/p>\n

B’s speed\u00a0 = (96 x 60 x 60 <\/u>\u00a0)km\/hr = 5.76 km\/hr.<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 60 x 1000<\/p>\n

Ex. 5. A, Band C \u00a0are three contestants in a km race. If A can give B a start of 40 m<\/strong><\/p>\n

\u00a0\u00a0\u00a0 and A can give C \u00a0a start of 64m\u00a0 how many metre’s\u00a0 start can B give C ?<\/strong><\/p>\n

\u00a0<\/strong>\u00a0\u00a0\u00a0\u00a0 Sol: <\/strong>\u00a0\u00a0While A covers 1000 m, B covers (1000 – 40) m = 960 m and<\/p>\n

\u00a0\u00a0\u00a0\u00a0 C covers (1000 – 64) m or 936 m.<\/p>\n

\u00a0When B covers 960 m, C covers 936 m.<\/p>\n

\u00a0Ex 6.<\/strong> In a game of 80 points; A can give B 5 points\u00a0 and C 15 \u00a0points. Then how many points \u00a0B can give C \u00a0in a game of 60 ?<\/strong><\/p>\n

\u00a0<\/strong>Sol.\u00a0\u00a0 <\/strong>\u00a0A: B = 80 : 75,\u00a0\u00a0 A : C = 80 : 65.<\/p>\n

B\/C\u00a0 = ( B\/ A *\u00a0 A\/C)\u00a0 = (75 \/ 80 * 80 \/ 65)\u00a0 = 15\/13 = 60 \/52 = 60: 5<\/p>\n

Therfore ,In a game of 60, B can give C\u00a0 8 points.<\/p>\n

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I can’t provide a free PDF download<\/strong> of RS Aggarwal\u2019s Quantitative Aptitude<\/strong> book as it is copyrighted. However, I can help you with Races and Games<\/strong> concepts, formulas, and practice questions based on RS Aggarwal’s book.<\/p>\n

\n

Important Formulas & Concepts for Races & Games<\/strong><\/h3>\n

Basic Terminologies<\/strong><\/p>\n

    \n
  • Race<\/strong>: A competition where contestants cover a fixed distance.<\/li>\n
  • Dead Heat<\/strong>: When all contestants finish the race at the same time.<\/li>\n
  • Start Advantage<\/strong>: If a racer gets a head start, it means they cover some distance before the race starts.<\/li>\n<\/ul>\n

    Formula for Races Between Two Persons<\/strong>
    \nIf A can give B \u2018d\u2019 meters in a race of \u2018D\u2019 meters, then the ratio of their speeds is:<\/strong><\/p>\n

    Speed\u00a0of\u00a0A:Speed\u00a0of\u00a0B=D:(D\u2212d)\\text{Speed of A} : \\text{Speed of B} = D : (D – d)<\/span>Speed\u00a0of\u00a0A<\/span><\/span>:<\/span><\/span>Speed\u00a0of\u00a0B<\/span><\/span>=<\/span><\/span>D<\/span>:<\/span><\/span>(<\/span>D<\/span>\u2212<\/span><\/span>d<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

    If A can give B \u2018t\u2019 seconds in a race, the ratio of their speeds is:<\/strong><\/p>\n

    Speed\u00a0of\u00a0A:Speed\u00a0of\u00a0B=(D\/(D\u2212d))\\text{Speed of A} : \\text{Speed of B} = (D \/ (D – d))<\/span>Speed\u00a0of\u00a0A<\/span><\/span>:<\/span><\/span>Speed\u00a0of\u00a0B<\/span><\/span>=<\/span><\/span>(<\/span>D<\/span>\/<\/span>(<\/span>D<\/span>\u2212<\/span><\/span>d<\/span>))<\/span><\/span><\/span><\/span><\/span><\/p>\n

    Race with a Start Advantage<\/strong><\/p>\n

      \n
    • If A gives B a start of \u2018d\u2019 meters<\/strong>, B runs D – d<\/strong> meters while A runs D<\/strong> meters.<\/li>\n
    • Speed ratio: Speed\u00a0of\u00a0A:Speed\u00a0of\u00a0B=D:(D\u2212d)\\text{Speed of A} : \\text{Speed of B} = D : (D – d)<\/span>Speed\u00a0of\u00a0A<\/span><\/span>:<\/span><\/span>Speed\u00a0of\u00a0B<\/span><\/span>=<\/span><\/span>D<\/span>:<\/span><\/span>(<\/span>D<\/span>\u2212<\/span><\/span>d<\/span>)<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n

      Games & Matches (Winning Probability Formula)<\/strong>
      \nIf two players A and B play a series of \u2018n\u2019 games, the probability of A winning \u2018m\u2019 times is:<\/strong><\/p>\n

      P=C(n,m)\u00d7pm\u00d7(1\u2212p)n\u2212mP = C(n, m) \\times p^m \\times (1-p)^{n-m}<\/span>P<\/span>=<\/span><\/span>C<\/span>(<\/span>n<\/span>,<\/span>m<\/span>)<\/span>\u00d7<\/span><\/span>p<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span>1<\/span>\u2212<\/span><\/span>p<\/span>)n<\/span>\u2212<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      where p = probability of A winning a single game<\/strong>.<\/p>\n

      \n

      \u00a0Sample Problems & Solutions<\/strong><\/h3>\n

      Q1:<\/strong> A can run 200m in 20s, and B can run 200m in 25s. How much start should A give B in a 200m race?
      \nQ2:<\/strong> In a 500m race, A beats B by 50m. Find the speed ratio of A to B.
      \nQ3:<\/strong> A can give B a start of 20m in a 200m race. If their speeds remain the same, how much start can A give B in a 500m race?<\/p>\n

      Would you like detailed solutions<\/strong> or more practice questions<\/strong>? Let me know!\u00a0<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

      RS Aggarwal Quantitative Aptitude PDF Free Download: RACES AND GAMES<\/h3>\n","protected":false},"excerpt":{"rendered":"

      RACES AND GAMES IMPORTANT FACTS \u00a0Races: A contest of speed in running, riding, driving, sailing or rowing is called race \u00a0Course: The ground or path on which contests are made is called a race course. \u00a0Starting Point: The point from which a race begins is known as a starting point. \u00a0Winning Point or Goal: The […]<\/p>\n","protected":false},"author":41,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[126,127],"tags":[],"class_list":["post-6016","post","type-post","status-publish","format-standard","hentry","category-rs-aggarwal-quantitative-aptitude","category-rs-aggarwal-quantitative-aptitude-pdf"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts\/6016","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/users\/41"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/comments?post=6016"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts\/6016\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/media?parent=6016"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/categories?post=6016"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/tags?post=6016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}