CBSE Class 10-Mathematics: Chapter –4 Quadratic Equations Part 22

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Question 2:

An express train takes 1 hour less than a passenger train to travel between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If, the average speed of the express train is more than that of the passenger train, find the average speed of two trains.

Answer:

Let average speed of passenger train

Let average speed of express train

Time taken by passenger train to cover hours

Time taken by express train to cover hours

According to the given condition,

Comparing equation with general quadratic equation , we get and

Applying Quadratic Formula

As speed cannot be in negative. Therefore, speed of passenger train

And speed of express train

Question 3:

Sum of areas of two squares is . If, the difference of their perimeters is metres, find the sides of the two squares.

Answer:

Let perimeter of first square metres

Let perimeter of second square metres

Length of side of first square meters {Perimeter of square = 4 × length of side}

Length of side of second square metres

Area of first square side side

Area of second square

According to given condition:

Comparing equation with standard form ,

We get and

Applying Quadratic Formula

Perimeter of square cannot be in negative.

Therefore, we discard .

Therefore, perimeter of first square metres

And Perimeter of second square metres

Side of First square

And Side of second Square