{"id":12346,"date":"2018-03-10T13:05:37","date_gmt":"2018-03-10T07:35:37","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=12346"},"modified":"2018-03-10T14:42:58","modified_gmt":"2018-03-10T09:12:58","slug":"cat-questions-races-solutions","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/cat-questions-races-solutions\/","title":{"rendered":"CAT Questions on Races With Solutions"},"content":{"rendered":"

CAT Questions on Races With Solutions:<\/strong><\/span><\/p>\n

Download CAT App to Access this on your mobile<\/a><\/p>\n

25 Mocks + 30 Sectionals for Rs. 1249<\/a><\/p>\n

Download CAT Quant Questions PDF<\/a><\/p>\n

Take Free Mock Test for CAT 2018<\/a><\/p>\n

Question 1:\u00a0<\/strong>In a 200 m race, Abhay beats Chetan by 40m and Chetan beats Kundan by 20 m. If Abhay and Kundan were to run a 500 m race, then by what distance will Abhay beat Kundan?<\/p>\n

a) 80m
\nb) 120m
\nc) 140m
\nd) 60m<\/p>\n

Question 2:\u00a0<\/strong>X, Y and Z ran a 50 m race. The time taken by X was recorded by watch W1 and the time taken by Y and Z was recorded by watch W2. The time taken by X, Y and Z to complete the race according to the respective watches used was 5, 6 and 3 seconds respectively. W2 is a faulty clock and loses time uniformly. If X beats Y by 10 m, what was the speed of Z during the race?<\/p>\n

a) 16
\nb) 17
\nc) 18
\nd) 19<\/p>\n

Question 3:\u00a0<\/strong>Two persons A and B are racing along a circular track. The speed of A is twice the speed of B. The length of the circular track is 800 m and the length of the race is 7200 m. After the start of the race, A meets B for the first time at the end of the third minute. If A and B start the race from the same point, find the time taken by A to finish the race.<\/p>\n

a) 19 minutes
\nb) 9.5 minutes
\nc) 27 minutes
\nd) 13.5 minutes<\/p>\n

Download CAT 2018 Syllabus PDF<\/a><\/p>\n

Question 4:\u00a0<\/strong>In 1 km race, in which A,B, C are running, A beats B by 100 m, B beats C by 100 m. In the next kilometer race, C starts at the starting line, B starts 100 m behind the starting line and A starts 100 m behind B. Find the distance (in m) by which the winner is ahead of the person just behind him.<\/p>\n

a) 20
\nb) 21
\nc) 22
\nd) 23<\/p>\n

Question 5:\u00a0<\/strong>Ram can beat Shyam by 40 meters in a race. If Ram starts from a point which is 20 metres behind the start line and Shyam starts from the start line, Ram will still beat Shyam by 24 metres. What is the length of their race?<\/p>\n

a) 100 m
\nb) 150 m
\nc) 200 m
\nd) 250 m
\ne) 500 m<\/p>\n

Solutions for\u00a0CAT Questions on Races With Solutions:<\/strong><\/span><\/p>\n

Solutions:<\/strong><\/p>\n

1) Answer (C)<\/strong><\/p>\n

In the time that Abhay runs 200 m, Chetan runs 160m so the ratio of speeds of Abhay and Chetan is 5:4
\nIn the time Chetan runs 200m, Kundan runs 180m. So the ratio of speeds of Chetan and Kundan is 10:9
\nThus we can say that in the time that Chetan runs 160m, Kundan runs 160*9\/10 = 144 m
\nThus in a 200 m race, Abhay will Kundan by 56m. Thus in a 500 m race, Abhay will beat Chandan by 56*2.5 = 140m<\/p>\n

Factors of a number – Formulas for CAT<\/a><\/p>\n

Formulas on Number system and factorials\u00a0<\/a><\/p>\n

2) Answer (A)<\/strong><\/p>\n

Speed of X = 50\/5 = 10 m\/s
\nSpeed of Y = 40\/5 = 8 m\/s
\nTime taken by Y to finish the race = 50\/8 = 6.25 s
\nIt is now known that the faulty clock lost time and has shown 6s instead of 6.25s for Y.
\nSimilarly the time taken by Z = 3 * 6.25\/6 = 3.125s
\nSpeed of Z = 50\/3.125 = 16 m\/s.<\/p>\n

3) Answer (D)<\/strong><\/p>\n

Let the speed of A be \u20182s\u2019 m\/s. Speed of B = \u2018s\u2019 m\/s
\nRelative speed between A and B = 2s – s = s m\/s
\nTime taken for A to meet B = length of the track \/ relative speed between A and B = 800 \/ s = 3 minutes
\n=> 800 \/ s = 180
\n=> s = 800\/180 m\/s
\nSo, time taken by A to finish the race = 7200 \/ 2*(800\/180) = 7200 * 180 \/ 2*800 = 9 * 90 seconds = 810 seconds = 13.5 minutes<\/p>\n

4) Answer (A)<\/strong><\/p>\n

Let the time taken by A = t
\nSpeed of A = 1000\/t
\nSpeed of B = 900\/t
\nSpeed of C = 900*9\/10\/t = 810\/t
\nTime taken by C in the second race = 100t\/81.
\nTime taken by B in the second race = 11t\/9.
\nTime taken by A in the second race = 12t\/10.
\nOut of these 12t\/10 is the lowest. Hence A wins the race.
\nB is the second in race.
\nDistance covered by B in 12t\/10 = 900\/t*12t\/10 = 1080
\nDistance = 1000+100-1080 = 20 m<\/p>\n

5) Answer (C)<\/strong><\/p>\n

Let the length of the race be l
\nIn the time that Ram travels l metres, Shyam travels l-40 metres.
\nIn the time that Ram travels l+20 metres, Shyam travels l – 24 metres.
\nFrom these two equations we can see that in the time that Ram travels 20 metres, Shyam travels 16 metres.
\nSo for every 20 metres travelled by Ram Shyam will be left behind by 4 metres.
\nThe final gap between Ram and Shyam is 40 metres, hence there has to be 10 intervals of such 20 metres.
\nHence the length of the race is 20*10 = 200 metres<\/p>\n

Take a free CAT online mock test<\/a><\/p>\n

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CAT Questions on Races With Solutions: Download CAT Quant Questions PDF Take Free Mock Test for CAT 2018 Question 1:\u00a0In a 200 m race, Abhay beats Chetan by 40m and Chetan beats Kundan by 20 m. If Abhay and Kundan were to run a 500 m race, then by what distance will Abhay beat Kundan? 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