One trader sold 120 meters of cloth at 10% profit and 90 meters of cloth at 16% profit. If he had sold all the clothes at a profit of 13%, he would have made a further profit of Rs 22.50. What is the purchase price of cloth per meter?
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An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, find the average speed of the two trains.
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Answer
Let x km per hour be the average speed of the passenger train, then the average speed of the express train will be (x+11) km per hour.
The time taken by the passenger train is
x
132
hour and the time taken by the express train is
(x+11)
132
hour. So,
x+11
132
=
x
132
+1
x
2
+11x−1452=0
x
2
+44x−33x−1452=0
(x−33)(x+44)=0
x=33,x=−44
The speed cannot be negative, so the speed of the passenger train is 33 km per hour and the speed of the express train is 33+11=44 km per hour.