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A train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/h from its usual speed. Find the usual speed of the train

Last updated at Oct. 1, 2019 by Teachoo

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Question 23 (OR 1
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A train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/h from its usual speed. Find the usual speed of the train

Transcript

Question 23 (OR 1st question) A train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/h from its usual speed. Find the usual speed of the train Let the speed of train be x km/hr Normal speed Distance = 300 km Speed = x km/hr Speed = π·ππ π‘ππππ/(ππππ πππππππ) x = 300/(ππππ πππππππ) Time original = 300/π₯ Speed 5 km/h more Distance = 300 km Speed = (x + 5) km/hr Speed = π·ππ π‘ππππ/(ππππ πππππ πΌππππππ ππ) x + 5 = 300/(ππππ πππππ πΌππππππ ππ) Time speed increased = 300/(π₯ + 5) Given that train takes 2 hours less after speed increased Time Speed increased = Time original β 2 hours 300/(π₯ + 5) = 300/π₯ β 2 2 = 300/π₯ β 300/(π₯ + 5) 300/π₯ β 300/(π₯ + 5) = 2 300(1/π₯β1/(π₯ + 5)) = 2 300(((π₯ + 5) β π₯)/(π₯(π₯ + 5))) = 2 300(5/(π₯(π₯ + 5))) = 2 300 Γ 5/2 = x (x + 5) 150 Γ 5 = x(x + 5) 750 = x(x + 5) 750 = x2 + 5x x2 + 5x = 750 x2 + 5x β 750 = 0 We factorize by splitting the middle term method x2 + 30x β 25 β 750 = 0 x (x + 30) β 25(x + 30) = 0 (x + 30) (x β 25) = 0 So, x = β30, x = 25 Splitting the middle term method We need to find two numbers whose Sum = 5 Product = β 750 Γ 1 = β 750 We know that Speed of train = x So, x cannot be negative β΄ x = 25 is the solution So, Speed of train = x = 25 km/hr We know that Speed of train = x So, x cannot be negative β΄ x = 25 is the solution So, Speed of train = x = 25 km/hr

CBSE Class 10 Sample Paper for 2019 Boards

Paper Summary

Question 1

Question 2 (Or 1st)

Question 2 (Or 2nd)

Question 3 (Or 1st)

Question 3 (Or 2nd)

Question 4

Question 5

Question 6

Question 7 (Or 1st)

Question 7 (Or 2nd)

Question 8 (Or 1st)

Question 8 (Or 2nd)

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16 (Or 1st)

Question 16 (Or 2nd)

Question 17 (Or 1st)

Question 17 (Or 2nd)

Question 18

Question 19 (Or 1st)

Question 19 (Or 2nd)

Question 20

Question 21 (Or 1st)

Question 21 (Or 2nd)

Question 22

Question 23 (Or 1st) You are here

Question 23 (Or 2nd)

Question 24

Question 25

Question 26

Question 27 (Or 1st)

Question 27 (Or 2nd)

Question 28 (Or 1st)

Question 28 (Or 2nd)

Question 29

Question 30

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.