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## Algebra Level 1 Test 3

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Question 1 |

A boy was asked of his age by his friend. The boy said, "The number you get when you subtractÂ 25 times my age from twice the square of my age willÂ be thrice your age." If the friend's age is 14, then the age of the boy is

A | 28 yr |

B | 21 yr |

C | 14 yr |

D | 25 yr |

Question 1 Explanation:

Let the age of boy be a yr.

2a

2a

2a(a - 14) +3(a â€“ 14)= 0

2a+3 = 0

a â€“ 14 = 0

a = 14

so the right option for the question is option c

2a

^{2}â€“ 25a = 3 x 142a

^{2}â€“ 25a - 42 = 02a(a - 14) +3(a â€“ 14)= 0

2a+3 = 0

a â€“ 14 = 0

a = 14

so the right option for the question is option c

Question 2 |

The product of the present ages of Sarita and Gauri is 320. Eight years from now, Sarita's age will be three times the age of Gauri. What was the age of Sarita when Gauri was born?

A | 40 yr |

B | 32 yr |

C | 48 yr |

D | 36 yr |

Question 2 Explanation:

Let the present ages of Sarita and Gauri be a and b.

Then according to the question

ab = 320

(a + 8) = 3(b + 8)

a â€“ 3b = 16

a â€“ 3(320/a) = 16

a

by solving the equation

i.e. a = 40 and b = 8

So Sarita was 32 at the time of Gauri born.

Then according to the question

ab = 320

(a + 8) = 3(b + 8)

a â€“ 3b = 16

a â€“ 3(320/a) = 16

a

^{2}â€“ 16a - 960 = 0by solving the equation

i.e. a = 40 and b = 8

So Sarita was 32 at the time of Gauri born.

Question 3 |

In a class, the number of girls is one less than the number of the boys. If the product of the number of boys and that of girls is 272, then the number of girls in the class is

A | 15 |

B | 14 |

C | 16 |

D | 17 |

Question 3 Explanation:

Let the number of girls and boys be a and b.

Then according to the question

a â€“ 1 = b

ab = 272

Then,

a (a - 1) = 272

a

by solving this

we get a = 16

Then according to the question

a â€“ 1 = b

ab = 272

Then,

a (a - 1) = 272

a

^{2 }- a - 272 = 0by solving this

we get a = 16

Question 4 |

Children were fallen-in for a drill. If each row contained 4 children less, 10 more rows would have been made. But if 5 more children were accommodated in each row the number of rows would have reduced by S. The number of children in the school is

A | 200 |

B | 150 |

C | 300 |

D | 100 |

Question 4 Explanation:

Let the number of rows and columns be a and b.

(b - 4)(a + 10)= ab

10b â€“ 4a = 40

And (b + 5)(a - 5) = ab

5a â€“ 5b = 25

a â€“ b = 5

a = 15

b = 10

Therefore the number of students = 15 x 10 = 150

(b - 4)(a + 10)= ab

10b â€“ 4a = 40

And (b + 5)(a - 5) = ab

5a â€“ 5b = 25

a â€“ b = 5

a = 15

b = 10

Therefore the number of students = 15 x 10 = 150

Question 5 |

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Sanchit paid Rs. 45 for a book kept for 7 days, while Karan paid Rs. 25 for the book he kept for 5 days. The fixed charge and the charge for each extra day is

A | Rs.Â 5 and Rs.Â 10 |

B | Rs. 10 and Rs. 10 |

C | Rs.Â 15 and Rs. 5 |

D | Rs.Â 5 and Rs.Â 15 |

Question 5 Explanation:

Let a be the fix charges for first three days

And b be the charges of extra days

a+ 4b=45â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦1

a +2b=25â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.2

so from 1 and 2

a = Rs. 5

b = Rs. 10

And b be the charges of extra days

a+ 4b=45â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦1

a +2b=25â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.2

so from 1 and 2

a = Rs. 5

b = Rs. 10

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