This question is taken from linear equations in two variables in which we have to find the speed of the train and the taxi if a person took 5 hrs 30 mins travel a distance of 300 km by train and 200 km by taxi and it took longer time if it travels 260 km by train and 240 km by taxi.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 33

## Let, the speed of trainÂ =xÂ km/h and the speed of the taxiÂ =yÂ km/h.

Now usingÂ Â time=distanceâ€‹/speed, we get,

300/x â€‹+ 200/yâ€‹=11â€‹/2Â Â Â ………..(1) and

260/x â€‹+ 240/y â€‹= 5+ 36/60 â€‹= 5+ 3/5â€‹=28/5â€‹Â Â Â ……….(2)

Let,Â x1â€‹Â =mÂ andÂ y1â€‹Â =nÂ then,

600m+400n=11Â Â ……….(3)

1300m+1200n=28Â Â ………(4)

Now, equationÂ (3)Ã—3âˆ’Â equationÂ (4)Ã—4Â we get,

500m=5

â‡’m=1/100â€‹

â‡’x=100Â km/h.

Putting the value ofÂ mÂ in equation (3) we get,

n=5/400â€‹=1/80â€‹

â‡’y=80Â km/h.

Speed of train =100Â km/h.

Speed of taxi =80Â km/h.