NCERT solution for class 10th maths: chapter-3 LINEAR EQUATIONS (Ex.3.1)

Question-1: Aftab tells his daughter, “Seven years ago I was seven times as old as you were then. and also three years from now, I shall be three times as old as you will be.” Represent this situation algebraically and graphically.
Solution:-   
"Seven years ago I was seven times as old as you were then." 

Let the present age of Aftab be ‘x’.
And, the present age of his daughter be ‘y’.

Seven years ago,
Age of Aftab = x-7
Age of his daughter = y-7

According to the question,
x − 7 = 7(y − 7)
x − 7 = 7y − 49
x − 7y = −42             ................................(i)

"three years from now, I shall be three times as old as you will be." 

Three years from now,
Age of Aftab will be ‘x+3’
Age of his daughter will be ‘y+3’

According to the question,
x + 3 = 3(y + 3)
x + 3 = 3y + 9
x -3y = 9-3
x − 3y = 6 .................................................(ii)

So, the algebraic representation of this situation is:
x − 7y = −42  ........................(i)
x − 3y = 6      ........................(ii)

x − 7y = −42 

Now second equation
x − 3y = 6

The graphical representation is-

Question 2: A cricket team coach purchases 3 bats and 6 balls for Rs 3900. Later on, he buys 1 bat and 3 more balls of the same kind for Rs 1300. Represent the situation algebraically and geometrically.
Solution:
Let cost of one bat = Rs x
Cost of one ball = Rs y

So, cost of 3 bats is 3x and cost of 6 balls is 6y and total cost is Rs 3900
now equation is
3x + 6y = 3900 ….................................. (i)

Dividing equation by 3, we get
x + 2y = 1300

So, cost of 1 bat is x and cost of 3 balls is 3y and total cost is Rs 1300
now equation is
x + 3y = 1300.................................. (ii)

So, the algebraic representation of this situation is:
3x + 6y = 3900 …......... (i) or x + 2y = 1300
x + 3y = 1300 …........... (ii)

first equation is x +2y = 1300

Second equation is x +3y = 1300

Now table

Graphical representation,

Question 3:The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.
Solution::
Let cost of 1 kg of apples = Rs x
Cost of 1 kg of grapes = Rs y

So, here the cost of 2 kg of apples is 2x and cost of 1kg of grapes is y. and total cost is Rs. 160.
now equation is
2x + y = 160..................... (i)

So, 4 kg of apples is 4x and 2kg of grapes is 2y. and total cost is Rs. 300.
now equation is
4x + 2y = 300....................(ii)

Dividing by 2 we get
2x + y = 150

So, the algebraic representation of this situation is:
2x + y = 160 …......... (i)
4x + 2y = 300 …........... (ii) or 2x + y = 150

 first equation is 2x +y = 160

Second equation is 2x +y = 150

Now table

Graphical representation:

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