**Question 1:**

*Astitva 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:**

Let the present age of Astitva be ‘x’.

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

Seven years ago,

Age of Astitva = x-7

Age of his daughter =y-7

According to the question,

Three years from now,

Age of Astitva will be ‘x+3’

Age of his daughter will be ‘y+3’

According to the question,

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

The algebraic equation is represented by

For

The solution table is

X |
-7 | 0 | 7 |

Y |
5 | 6 | 7 |

For

The solution table is

X |
6 | 4 | 0 |

Y |
0 | -1 | -2 |

The graphical representation is-

**Question 2:**

*A cricket team coach purchases 3 bats and 3 balls for Rs 3900. Later on, he buys 1 bat and 2 more balls of the same kind for Rs 1200. Represent the situation algebraically and geometrically.*

**Solution:**

Let us assume that the cost of a bat be ‘Rs x’

And,the cost of a ball be ‘Rs y’

According to the question, the algebraic representation is

For

The solution table is

x |
300 | 100 | -100 |

y |
500 | 600 | 700 |

For,

The solution table is

x |
300 | 100 | -100 |

y |
500 | 600 | 700 |

The graphical representation is as follows.

**Question 3:**

**The cost of 2 kg of apples and 1 kg 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 given situation algebraically and geometrically.**

**Solution:**

Let the cost of 1 kg of apples be ‘Rs x’

And, cost of 1 kg of grapes be ‘Rs y’

According to the question, the algebraic representation is

For,

The solution table is

X |
50 | 60 | 70 |

Y |
60 | 40 | 20 |

For

The solution table is

x |
70 | 80 | 75 |

y |
10 | -10 | 0 |

The graphical representation is as follows.