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# Formulate the following problems as a pair of equations, and hence find their solutions: (iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately. Q.2(3)

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The steps of solving this important question for Pair of Linear Equations in Two Variables, Of class 10th in easy method Formulate the following problems as a pair of equations, and hence find their solutions: (iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

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1. Let us consider,

Speed of the train = x km/h

Speed of the bus = y km/h

According to the given question,

60/x + 240/y = 4 â€¦â€¦â€¦â€¦â€¦â€¦â€¦(1)

100/x + 200/y = 25/6 â€¦â€¦â€¦â€¦â€¦.(2)

Put 1/x=m and 1/y=n, in the above two equations;

60m + 240n = 4â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..(3)

100m + 200n = 25/6

600m + 1200n = 25 â€¦â€¦â€¦â€¦â€¦â€¦â€¦.(4)

Multiply eq.3 by 10, to get,

600m + 2400n = 40 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(5)

Now, subtract eq.4 from 5, to get,

1200n = 15

n = 15/1200 = 1/80

Substitute the value of n in eq. 3, to get,

60m + 3 = 4

m = 1/60

m = 1/x = 1/60

x = 60

And y = 1/n

y = 80

T

herefore,

Speed of the train = 60 km/h

Speed of the bus = 80 km/h

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