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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. Q.1

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I am finding some problem on solving this question. Its time taking question. So i want best option for solving this question. 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.

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  1. Let the present age of Aftab be ‘x’.

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

    Now, we can write, 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)

    Also, three years from now or after three years,

    Age of Aftab will become = x+3.

    Age of his daughter will become = y+3

    According to the situation given,

    x+3 = 3(y+3)

    ⇒x+3 = 3y+9

    ⇒x−3y = 6       …………..…………………(ii)

    Subtracting equation (i) from equation (ii) we have

    (x−3y)−(x−7y) = 6−(−42)

    ⇒−3y+7y = 6+42

    ⇒4y = 48

    ⇒y = 12

    The algebraic equation is represented by

    x−7y = −42

    x−3y = 6

    For, x−7y = −42 or x = −42+7y

    The solution table is

    Ncert solutions class 10 chapter 3-1

    For,  x−3y = 6   or     x = 6+3y

    The solution table is

    Ncert solutions class 10 chapter 3-2

    The graphical representation is:

    Ncert solutions class 10 chapter 3-3

     

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