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Question 23 (OR 1 st 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

A train takes 2 hours less for a journey of 300 km if its speed is

Question 23 (Or 1st) - CBSE Class 10 Sample Paper for 2019 Boards - Part 2
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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·π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’/(π‘‡π‘–π‘šπ‘’ π‘œπ‘Ÿπ‘”π‘–π‘›π‘Žπ‘™) x = 300/(π‘‡π‘–π‘šπ‘’ π‘œπ‘Ÿπ‘”π‘–π‘›π‘Žπ‘™) Time original = 300/π‘₯ Speed 5 km/h more Distance = 300 km Speed = (x + 5) km/hr Speed = π·π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’/(π‘‡π‘–π‘šπ‘’ 𝑆𝑝𝑒𝑒𝑑 πΌπ‘›π‘π‘Ÿπ‘’π‘Žπ‘ π‘’π‘‘) x + 5 = 300/(π‘‡π‘–π‘šπ‘’ 𝑆𝑝𝑒𝑒𝑑 πΌπ‘›π‘π‘Ÿπ‘’π‘Žπ‘ π‘’π‘‘) Time speed increased = 300/(π‘₯ + 5) Given that train takes 2 hours less after speed increased Time Speed increased = Time original – 2 hours 300/(π‘₯ + 5) = 300/π‘₯ – 2 2 = 300/π‘₯ – 300/(π‘₯ + 5) 300/π‘₯ – 300/(π‘₯ + 5) = 2 300(1/π‘₯βˆ’1/(π‘₯ + 5)) = 2 300(((π‘₯ + 5) βˆ’ 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 – 750 = 0 We factorize by splitting the middle term method x2 + 30x – 25 – 750 = 0 x (x + 30) – 25(x + 30) = 0 (x + 30) (x – 25) = 0 So, x = –30, x = 25 Splitting the middle term method We need to find two numbers whose Sum = 5 Product = – 750 Γ— 1 = – 750 We know that Speed of train = x So, x cannot be negative ∴ 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 ∴ x = 25 is the solution So, Speed of train = x = 25 km/hr

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.