# 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

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.

#### Solution

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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 :

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.

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Solve the following system of equations by cross-multiplication method ax + by = 1;  bx + ay = \frac{(a+b)^{2}}{a^{2}+b^{2}-1

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

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

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Solve the following system of equations by cross-multiplications method.

a(x + y) + b (x – y) = a^2 – ab + b^2

a(x + y) – b (x – y) = a^2 + ab + b^2

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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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