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  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
  2. Serial order wise
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Ex 3.7, 3 A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train. Let Speed of train = x km/h & Time taken = y hours. We know that, Speed = ๐ท๐‘–๐‘ ๐‘ก๐‘Ž๐‘›๐‘๐‘’/๐‘‡๐‘–๐‘š๐‘’ Distance = Speed ร— Time Distance = xy If the train would have been 10 km/h faster I.e. Speed = x + 10 It would have taken 2 hours less i.e. Time = y โˆ’ 2 Now, Distance = Speed ร— time Distance = (x + 10) (y โˆ’ 2) Putting Distance = xy from equation (1) xy = (x + 10) (y โˆ’ 2) xy = x (y โˆ’ 2) + 10 (y โˆ’ 2) xy = xy โˆ’ 2x + 10y โˆ’ 20 2x โˆ’ 10y + 20 = xy โˆ’ xy 2x โˆ’ 10y + 20 = 0 Also, If the train were slower by 10 km/h Speed = x โˆ’ 10, it would have taken 3 hours more Time = y + 3. Now Distance = Speed ร— time Distance = (x โˆ’ 10) (y + 3) Putting Distance = xy from equation (1) xy = (x โˆ’ 10) (y + 3) xy = x (y + 3) โˆ’ 10y โˆ’ 30 xy = xy + 3x โˆ’ 10y โˆ’ 30 xy โˆ’ xy = 3x โˆ’ 10y โˆ’ 30 3x โˆ’ 10y โˆ’ 30 = 0 Hence, the equations are 2x โˆ’ 10y + 20 = 0 โ€ฆ(2) 3x โˆ’ 10y โˆ’ 30 = 0 โ€ฆ(3) From equation (2) 2x โˆ’ 10y + 20 = 0 2 (x โˆ’ 5y + 10) = 0 x โˆ’ 5y + 10 = 0 x = 5y โˆ’ 10 Putting (4) in equation (3) 3x โˆ’ 10y โˆ’ 30 = 0 3 (5y โˆ’ 10) โˆ’ 10y โˆ’ 30 = 0 15y โˆ’ 30 โˆ’ 10y โˆ’ 30 = 0 5y โˆ’ 60 = 0 5y = 60 y = 60/5 y = 12 Putting y = 12 in equation (4) x = 5y โˆ’ 10 x = (5 ร— 12) โˆ’ 10 x = 60 โˆ’ 10 x = 50 Therefore, speed of the train = 50 km/ h and time taken by the train = 12 hours Now, the distance covered by the train = Speed ร— time Distance = 50 ร— 12 Distance = 600 km Thus, Speed of train = x = 50 km/ h & Time taken by the train = y = 12 hours Now, Distance = Speed ร— time Distance = 50 ร— 12 Distance = 600 km

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CA Maninder Singh is a Chartered Accountant for the past 7 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
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