Ncert Solutions for Class 10 Maths

Exercise 3.5
(Cross Multiplication Method)
1. Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.
(i) x– 3y– 3 = 0 & 3x– 9y– 2 = 0 (ii) 2x+ y = 5 & 3x+ 2y = 8 (iii) 3x– 5y = 20 & 6x– 10y = 40 (iv) x– 3y– 7 = 0 & 3x– 3y – 15 = 0.
2. (i) For which values of a and b does the following pair of linear equations have an infinite number of solutions? 2x+ 3y = 7 & (a– b) x + (a+ b) y = 3a+b–2.
(ii) 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.

3. Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x+ 5y = 9 & 3x+ 2y = 4.
4. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
(i) 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.
(ii) A fraction becomes when 1 is subtracted from the numerator and it becomes when 8 is added to its denominator. Find the fraction.
(iii) 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?
(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
(v) 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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Cross Multiplication Method (Video) [Full Exercise 3.5]