# Aptitude - Races and Games - Discussion

### Discussion :: Races and Games - General Questions (Q.No.3)

3.

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 wins by:

 [A]. 60 m [B]. 40 m [C]. 20 m [D]. 10 m

Explanation:

To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.

While A covers 3 m, B covers 4 m.

 While A covers 360 m, B covers 4 x 360 m = 480 m. 3

Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind. A wins by 20 m.

 Kriti said: (Dec 3, 2010) Hi, when 3:4 is the ratio of speeds how can we use it as 3m and 4m for A and B resp.?

 Sudheer said: (May 19, 2011) Hi kriti here speed and distance are directly proportinal. If his speed is 10km/hr he cover 10km distance. If speed is 20km/hr he can cover 20 km distance. Thus speed and distance are directly proportinal. So here distance ratios also become3:4. But the time ratio will become4:3 because time and speed are inversly proportinal.

 Vamsi said: (Jul 5, 2011) I didn't understand how it can be 4/3. ?

 Malli said: (Sep 30, 2011) Hai, my dout is same that of vamsi. Why we had taken 4/3 in problem?

 Manojit said: (Feb 9, 2012) While A covers 3 m, B covers 4 m. While A covers 1m, B covers 4/3 m. While A covers 360 m, B covers (4/3* 360)m =480 m. Here time is same in case of speed.we count different distance in same time.

 Rajesh said: (Feb 7, 2013) Can be solved by simple calculation. A covers 360m (ie) 500-140. Ratio of speeds of A:B = 3:4. Let us consider A covers 3m/sec & B covers 4m/sec. Time taken by A to cover 360m=(360/3)=120seconds. So,Distance covered by B in 120s =120*4=480m. Therefore,A wins by 20 metres which is (500-480).

 Srinu said: (Feb 8, 2015) Time = dis\speed. T = 360\3 = 120sec. Now dis = sxT = 4x120 = 480m. So 500-480 = 20m. This is the answer.

 Newstein Faraday . said: (Jul 1, 2015) A has to travel 360 meters therefore Time =distance/ speed. So 360/3 = 120 seconds. The same 120 seconds b has to travel so distance = speed x time = 4 x 120 = 480. The remaining distance that b has to travel is 500-480 = 20.

 Damini.Arora said: (Aug 25, 2015) Here, because A has a start of 140, he has already covered 140 m when B starts. So when A covers rest of 360, B covers 480. Hence B loses race by 20 m.

 Ash said: (Jan 19, 2016) Speed is directly proportional to distance. 3/4 = (500-140)/(500-x). 3/4 = 360/(500-x). Hence x = 20.

 Anand said: (Sep 1, 2019) Here is the simplest method, Speed ratio is 3:4 SO let consider 3m & 4m for both A & B. A travels 360 and B travels 500. This means A takes 120 seconds and B takes 125 seconds. 5 seconds more than A is travelled by B. In one B travels 4m. So in 5 seconds, 5*4=20m. B travels 20m more than A. That is A win by 20m.

 Bkd said: (Dec 1, 2020) 3/4 = (500-140)/x. x = 480. Thus, In 500 m race, A gives B by 20m i.e.500-480.

 Anupcherry said: (Jun 29, 2021) A : B =140M. 3X + 4X =7X, 140/7 = 20M.