# Solution - Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method

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ConceptAlgebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method

#### Question

A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the
stream.

#### Solution

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A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?

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Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

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The time taken by a person to cover 150 km was 2 1/2 hours more than the time taken in the return journey. If he returned at a speed of 10 km/hour more than the speed while going, find the speed per hour in each direction.

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A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.

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For which value of k will the following pair of linear equations have no solution?

3x + y = 1

(2k – 1) x + (k – 1) y = 2k + 1

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#### Reference Material

Solution for concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method. For the courses 8th-10th CBSE, 9th - 10th SSC (English Medium)
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