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Pair of Linear Equations in Two Variables
Form the pair of linear equations for the following problems and find ...

Form the pair of linear equations for th | Class 10 Mathematics Chapter Pair of Linear Equations in Two Variables, Pair of Linear Equations in Two Variables NCERT Solutions

Welcome to the NCERT Solutions for Class 10 Mathematics - Chapter Pair of Linear Equations in Two Variables. This page offers a step-by-step solution to the specific question from Exercise 3, Question 3: . With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.

Question 3:

Form the pair of linear equations for the following problems and find their solution by substitution method.
(i) The difference between two numbers is 26 and one number is three times the other. Find them.
(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later, she buys 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.

(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
(v) A fraction becomes, , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes Find the fraction.

(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Answer:

(i) Let the numbers be x and y, such that x > y

Therefore, according to question

x - y = 26 …………….(1)

x = 3y…………….(2)

Putting the value of x from equation (2) to equation (1), we get

3y – y = 26

2y = 26

y = 13

Putting the value in equation (2), we get

x = 3 x 13

x = 39

Hence, the numbers are 39 and 13.

(ii) Let one be x◦ and other be y◦ such that (x◦ > y◦)

Therefore, according to question

x◦ + y◦ = 180◦…………….(1) (Supplementary angles)

x◦ = 18 + y◦…………….(2)

Putting the value of x from equation (2) to equation (1), we get

18 + y◦ + y◦ = 180◦

2y◦ = 162◦

Putting the value of y in equation (2), we get

x◦ = 18 + 81

x = 99

(iv) Let the fixed charge be = ₨ x

Let the charge for 1 km distance be = ₨ y

According to first condition,

x + 10y = ₨ 105

x = 105 – 10y …………….(1)

According to second condition,

x + 15y = 155 ………………(2)

Putting the value of x in equation (2), we get

105 – 10y + 15y = 155

5y = 50

y = 10

Putting the value of y in equation (2), we get

x + 15 x 10 = 155

x = 5

Hence, the fixed charge for taxi is ₨ 5 and, the charge for one km distance is ₨ 50.

Charge for 25 km distance

= 25 x 10 + 5

= ₨ 255

(vi) Let the age of Jacob be = x years

Let the age of Jacob’s father be = y years

After 5 years,

Jacob’s age x + 5 years

Son’s age y + 5 years

According to question,

x + 5 = 3 (y + 5)

x + 5 = 3y + 15

x = 3y + 10………………(1)

Five years ago,

(x- 5) = 7 (y - 5)

x – 5 = 7y – 35

x – 7y = -30……………….(2)

Putting the value of x in equation (2), we get

3y + 10 - 7y = -30

-4y = -40

y = 10

Putting the value of y in equation (1), we get

x = 3 (10) + 10

x = 40

Hence, the present age of Jacob is 40 years and the age of his son is 10 years.

Other Questions of Chapter Pair of Linear Equations in Two Variables

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Solve the following pair of linear equations by the substitution method.

Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is
36 m. Find the dimensions of the garden.

Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines (ii) parallel lines (iii) coincident lines

The coach of a cricket team buys 3 bats and 6 balls for ` 3900. Later, she buys another bat and 3 more balls of the same kind for ` 1300. Represent this situation algebraically and geometrically.

The cost of 2 kg of apples and 1kg of grapes on a day was found to be ` 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ` 300. Represent the situation algebraically and geometrically.

Popular questions of class 10 Mathematics

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:

(i) 2x²– 3x + 5 = 0 (iii) 2x²– 6x + 3 = 0

Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

Find two consecutive positive integers, sum of whose squares is 365.

Find two numbers whose sum is 27 and product is 182.

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Refer to Example 13. (i) Complete the following table:

(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability

Do you agree with this argument? Justify your answer.

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x² – 2x – 8 (ii) 4s² – 4s + 1 (iii) 6x² – 3 – 7x (iv) 4u² + 8u (v) t²– 15 (vi) 3x²– x – 4

Is it possible to design a rectangular park of perimeter 80 m and area 400 m²? If so, find its length and breadth.

Recently Viewed Questions of Class 10 Mathematics

Suppose you drop a die at random on the rectangular region shown in Fig. 15.6. What is the probability that it will land inside the circle with diameter 1m?

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.

Represent the following situations in the form of quadratic equations :
(i) The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(ii) The product of two consecutive positive integers is 306. We need to find the integers.
(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠ POA is equal to
(A) 50° (B) 60°
(C) 70° (D) 80°

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3.

Find the number of blue balls in the jar.

Find two consecutive positive integers, sum of whose squares is 365.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

On dividing x³– 3x²+ x + 2 by a polynomial g(x), the quotient and remainder were x – 2 nd –2x + 4, respectively. Find g(x).

(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective ?

Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Pair of Linear Equations in Two Variables.
Review previous year question papers to get an idea of how such questions may be framed in exams.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

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