# NCERT book Solutions for Class 10th Maths: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

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

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