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## Algebra Level 2 Test 6

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Question 1 |

If 6 yr are subtracted from the present age of Richa and the remainder is divided by 18, then the present age of her grandson Arth is obtained. If Arth is 2 yr younger to Malocha, whose age is 5 yr, then what is the age of Richa ?

84 yr | |

96 yr | |

48 yr | |

60 yr |

Question 1 Explanation:

Given that the age of Malocha = 5 yrs

Present age of Arth = 3 years

Now present age of Richa = 3 x 18 + 6 = 60

Present age of Arth = 3 years

Now present age of Richa = 3 x 18 + 6 = 60

Question 2 |

1 yr ago, a mother was 4 times older to her son. After 6 yr, her age becomes more than double her son’s age by 5 yr. The present ratio of their age will be

13 : 12 | |

3: 1 | |

11: 3 | |

25: 7 |

Question 2 Explanation:

Let the present age of mother = p years

Let the present age of son = q years

Therefore from the question we can say that

(p – 1) = 4 (q – 1 )

p = 4q -3 …………………………………….1

and p + 56 = 2 (q + 6) + 5

p = 2q + 11 ………………………………… 2

from the above two equations we can say that

4q – 3 = 2q + 11

On solving we get the values of p and q

i.e. p = 25 years

q = 7 years

so the ratio is 25 : 7

Let the present age of son = q years

Therefore from the question we can say that

(p – 1) = 4 (q – 1 )

p = 4q -3 …………………………………….1

and p + 56 = 2 (q + 6) + 5

p = 2q + 11 ………………………………… 2

from the above two equations we can say that

4q – 3 = 2q + 11

On solving we get the values of p and q

i.e. p = 25 years

q = 7 years

so the ratio is 25 : 7

Question 3 |

25 bags of wheat each weighing 40 kg costs Rs. 2750. Find the cost of 35 bags of wheat if each bag weighs 50 kg.

Rs. 5812.50 | |

Rs. 6212.50 | |

Rs. 4812.50 | |

Rs.3812.50 |

Question 3 Explanation:

Given the cost of wheat = 2750

So the price of one bag would be = (2750 / 25 x 40) = 2.75

Now the price of 35 bags which is of 50 kg = {2.75 / 50 x 35} = Rs. 4812.50

So the price of one bag would be = (2750 / 25 x 40) = 2.75

Now the price of 35 bags which is of 50 kg = {2.75 / 50 x 35} = Rs. 4812.50

Question 4 |

If f (0, 1) = 1, f (1, 2) = 5 ................., f (5, 6) = 61, then what is the value of f (7, 8)?

56 | |

112 | |

113 | |

117 |

Question 4 Explanation:

As we can see that f (0, 1) = 1 = which is 0

Similarly = f(1,2) = 1

So on: hence value of f(7,8 ) = 49+64= 113

^{2}+ 1^{2}= 1Similarly = f(1,2) = 1

^{2}+ 2^{2}= 5So on: hence value of f(7,8 ) = 49+64= 113

Question 5 |

A farmer has decided to build a wire fence along one straight side of his property. For this, he planned to place several fence-posts at 6 m intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was 5 less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them 8 m apart. What is the length of the side of his property and how many posts did he buy?

100 m, 15 | |

100 m, 16 | |

120 m, 15 | |

120 m, 16 |

Question 5 Explanation:

Let the side of the property = p m

Let the number of the posts that farmer bought = q

So when the space is 8 m

Posts will be

= p/8 +1 = q

= and when the space between is 6 m

Posts will be = p/6 +1 –y + 5

From these both the equations

p/8 – p/6 = -5

{(3 – 4)p}/24 = -5

-p/24 = -5

p = 120m

q = 16

Let the number of the posts that farmer bought = q

So when the space is 8 m

Posts will be

= p/8 +1 = q

= and when the space between is 6 m

Posts will be = p/6 +1 –y + 5

From these both the equations

p/8 – p/6 = -5

{(3 – 4)p}/24 = -5

-p/24 = -5

p = 120m

q = 16

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