Class 10
Linear Equations in Two Variables
Answer the questions:
(1) If thrice the daughter's age in years is added to mother's age, the sum is 62. If thrice the mother's age is
added to the daughter's age, the sum is 122. Find the age of mother and daughter.
(2) Two numbers are in ratio 2:1. If 4 is subtracted from both the numbers, ratio becomes 3:1. Find the
numbers.
(3) Which of the following conditions is true if the system of equations below is shown to be inconsistent
\[\begin{array}{l}{a_1}x + {b_1}y + {c_1} = 0\\{a_2}x + {b_2}y + {c_2} = 0\end{array}\]
| \[(a)\,\,\frac{{{a_1}}}{{{b_1}}} = \frac{{{a_2}}}{{{b_2}}} \ne \frac{{{c_1}}}{{{c_2}}}\] | \[(b)\,\,\frac{{{a_1}}}{{{a_2}}} \ne \frac{{{b_1}}}{{{b_2}}} \ne \frac{{{c_1}}}{{{c_2}}}\] | \[(c)\,\,\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} \ne \frac{{{c_1}}}{{{c_2}}}\] | \[(d)\,\,\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} = \frac{{{c_1}}}{{{c_2}}}\] |
(4) 12 chairs and 10 tables cost Rs. 7800 and 4 chairs and 5 tables cost Rs. 3100. Find the cost of one chair and one table separately.
(5) Sita is 6 years older than her friend Ashish. Sita's father is twice as old as Sita and Ashish is twice as old as his sister. The age of Sita's father is 39 years more than the age of Ashish's sister. Find the ages of Sita and Ashish.
(6) Which of the following equations has a unique solution?
5x + 2y + 17 = 0, 10x + 4y + 14 = 0
5x + 2y + 8 = 0, 15x + 6y + 18 = 0
5x + 2y + 8 = 0, 10x + 4y + 16 = 0
5x + 2y + 8 = 0, 10x + 4y + 17 = 0
(7) Four years ago George was four times older than his daughter. After four years, George will be 2 years
more than two times the age of his daughter. Find the present age of George and his daughter.
(8) Find value of k such that equations − x + 3y − 3 = 0 and − 3x + ky − 9 = 0, represents coincident lines.
(9) It is given that the sum of digits of a two digit number is 13. If 27 is added to the number, the digits interchange their place. Find the number.
(10) A two digit number is 6 more than 4 times the sum of its digits. If 27 is added to the number, the digit interchange their places. Find the number.
Choose correct answer(s) from the given choices
(11) The pair of equations − 3x − y + 2 = 0 and − 6x − 4y + 6 = 0 have
| a. no solution | b. a unique solution | c. exactly two solutions | d. infinitely many solutions |
(12) The pair of equations x = −3 and x = −8 has
| a. no solution | b. infinitely mainy solution | c. two solutions | d. an unique solution |
(13) For which value of p, following pair of linear equations have no solution.
p x + y = p² and x + p y = 1
(14) For which value of λ, following pair of linear equations have infinitely many solutions.
λ x + 12 y = λ and 3 x + λ y = λ − 3
Answers:
(1) 38 and 8 years
(2) 16 and 8
(3)
(4) Rs. 400 and Rs. 300
(5) 24 years and 18 years
(6) 5x + 2y + 17 = 0, 10x + 4y + 14 = 0
(7) 24 years and 9 years
(8) 9
(9) 58
(10) 58
(11) b. a unique solution
(12) a. no solution
(13) c. −1
(14) c. 6
Class 10th linear equations in two variables QUIZ
