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NCERT Solutions for Class 10th Maths Chapter 3:Linear Equations





1. 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.
2. The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 3 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.
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 Rs300.   . Represent this situation algebraically and geometrically.
Solution 1:
Let  age of Aftab is represented by x
 And age of daughter is represented by y
Then Seven years ago,
Age of Aftab               = x -7
Age of daughter         = y-7
As per the question Aftab  was seven times as old as her daughter then were  so we get
(x – 7) = 7 (y – 7)
x – 7y = -42                           …(1)
   Now Three years from now ,
Age of Aftab               = x +3
Age of daughter         = y+3
As per question Aftab  shall be three times as old as her daughter will be so we get
x + 3 = 3 (y + 3)
          x -3 y = 6                                  …(2)
Algebraic representation  of situation
x – 7 y = - 42                           …(1)
 x -3 y = 6                                  …(2)
To represent it graphically, we need to plot these equation  on the XY coordinate system.
We can choose two values of each equation and plot it on XY coordinate system
x – 7 y = - 42            or
y=(x+42)/7
X
0
7
Y=(x+42)/7
6
7
 x -3 y = 6
y=(x-6)/3
X
0
6
Y=(x-6)/3
-2
0

We can plot these two lines on XY coordinate system using the two point derived above
NCERT Solutions for Class 10th Maths Chapter 3:Linear Equations
Solution 2:
Let Cost of one bat    = Rs x
Let Cost of one ball    = Rs y
3 bats and 6 balls for Rs 3900 So that
3 x + 6y = 3900                     … (1)
Given that she buys another bat and 2 more balls of the same kind for Rs 1300
So we get
x + 2 y = 1300                       … (2)
Algebraic representation  of situation
3 x + 6y = 3900                     … (1)
x + 2 y = 1300                         … (2)
 To represent it graphically, we need to plot these equation  on the XY coordinate system.
We can choose two values of each equation and plot it on XY coordinate system
3x +6y = 3900                     or
y=(3900-3x)/6
X
-1300
1300
y=(3900-3x)/6
1300
0
 x +2 y = 1300
y=(1300-x)/2
X
1300
-1300
y=(1300-x)/2
0
1300
NCERT Solutions for Class 10th Maths Chapter 3:Linear Equations
Solution 3:
Let cost each kg of apples   = Rs x
Cost of each kg of grapes    = Rs y
The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160
So that
2 x + y             = 160              … (1)
Given that the cost of 4 kg of apples and 2 kg of grapes is Rs 300
 so we get
4x + 2y= 300               … (2)
Algebraic representation  of situation
2 x + y             = 160              … (1)
4x + 2y= 300               … (2)
To represent it graphically, we need to plot these equation  on the XY coordinate system.
We can choose two values of each equation and plot it on XY coordinate system
2x +y = 160              or
y=160-2x
X
80
40
y=160-2x
0
80
4x + 2y= 300           y=(300-4x)/2
X
0
50
y=(300-4x)/2
150
50
NCERT Solutions for Class 10th Maths Chapter 3:Linear Equations
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