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## Algebra Level 2 Test 9

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Question 1 |

A person brought 5 tickets from a station P to a station Q and 10 tickets from the station P to a station R. He paid Rs. 350. If the sum of a ticket from P to Q and from P to R is Rs. 42, then what is the fare from P to Q

12 | |

14 | |

16 | |

18 |

Question 1 Explanation:

Let the fares of both the stations i.e. from P to Q and from P to R Â be = a and b

So from the question we can say that

5a + 10b = 350â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..1

And a + b = 42â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦2

From equation 1 and 2

5a =70

a = 70/5 = 14

So from the question we can say that

5a + 10b = 350â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..1

And a + b = 42â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦2

From equation 1 and 2

5a =70

a = 70/5 = 14

Question 2 |

In a class room there are certain numbers of benches. If 6 students are made to sit on a bench then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then after accommodating all of them, space for 5 students is left. What is the total number of students in the class?

30 | |

42 | |

72 | |

cannot determine |

Question 2 Explanation:

Let the number of boys in the class = p

Let the number of girls in the class = q

pq + qp = 1600

pq = 800 from the question we are given by that

p +q = 60

by solving the equations

pÂ = 40 or 20

Since there are two values of p, we cannot determine the answer.

Let the number of girls in the class = q

pq + qp = 1600

pq = 800 from the question we are given by that

p +q = 60

by solving the equations

pÂ = 40 or 20

Since there are two values of p, we cannot determine the answer.

Question 3 |

For which of the following value of p the 2p

^{2}+6p <3 is satisfied?p < -3 and p > 1/2 | |

-3 < p < 1/2 | |

-1/2 | |

Â½ |

Question 3 Explanation:

2p

= 2p

= 2p(p +3) â€“ 1(p +3) < 0

= (2p -1) (p +3) < 0

This is possible only when either (2p -1) > 0 and (p+3) <0 or (2p -1) < 0 and (p+3) >0

This means there will be two cases

(2p -1) > 0 = x <1/2 and (p+3) <0 = p > -3 which is possible

So option (b) satisfies the condition.

^{2}+6p <3 = 2p^{2}+6p â€“ 3 < 0= 2p

^{2}+6p â€“p-3 <0= 2p(p +3) â€“ 1(p +3) < 0

= (2p -1) (p +3) < 0

This is possible only when either (2p -1) > 0 and (p+3) <0 or (2p -1) < 0 and (p+3) >0

This means there will be two cases

(2p -1) > 0 = x <1/2 and (p+3) <0 = p > -3 which is possible

So option (b) satisfies the condition.

Question 4 |

In a certain party, there was a bowl of rice for every two guests, a bowl of broth for every three of them and a bowl of meat for every four of them. If in all there were 65 bowl of food, then how manyÂ guests were in the party

65 | |

24 | |

60 | |

48 |

Question 4 Explanation:

Let the number of rice bowl , broth bowl and meat bowl = p ,q, r respectively

Therefore p + q+ r = 65

It is given that 2p = 3y = 4z

From these equations, we get the value of p = 30,q= 20 and r = 15

Therefore the total number of guests are = 60

Therefore p + q+ r = 65

It is given that 2p = 3y = 4z

From these equations, we get the value of p = 30,q= 20 and r = 15

Therefore the total number of guests are = 60

Question 5 |

If the value of p

^{11}= q^{0 }andÂ p = 2q , then what will be the value of q?1/2 | |

1 | |

-1 | |

-2 |

Question 5 Explanation:

Given that p

But we know that any number raised to the power 0 is one so q

That means p

P = 1

And now we are given by that

p = 2q

q = Â½ option number (a)

^{11}= q^{0}But we know that any number raised to the power 0 is one so q

^{0}= 1That means p

^{11}= 1P = 1

And now we are given by that

p = 2q

q = Â½ option number (a)

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