- In a market survey, 20% opted for product A whereas 60% opted for product B. The remaining individuals were not certain. If the difference between those who opted for product B and those who were uncertain was 720, how many individuals were covered in the survey ?

A. | 1440 | |

B. | 1800 | |

C. | 3600 | |

D. | Data inadequate. |

**Answer & Explanation**

**Answer: **Option **B**

**Explanation:**

Percentage of uncertain individuals = [100 – (20 + 60)]% = 20%.

60% of x – 20% of x = 720

<=> 40% of x = 720

<=> 40100x=720

<=> x=(720∗10040)=1800.

- A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are :

A. | 300 | |

B. | 500 | |

C. | 800 | |

D. | 1000 |

**Answer & Explanation**

**Answer: **Option **B**

**Explanation:**

Let the maximum marks he x.

Then, 33% of x = 125 + 40

<=> 33100x=165

<=> x=(165∗10033)=500.

- 8% of the people eligible to vote are between 18 and 21 years of age. In an election, 85% of those eligible to vote, who were between 18 and 21, actually voted. In that election, the number of persons between 18 and 21, who actually voted, was what percent of those eligible to vote ?

A. | 4.2 | |

B. | 6.4 | |

C. | 6.8 | |

D. | 8 |

Answer & Explanation

Answer: Option C

Explanation:

Let the number of persons eligible to vote be x. Then,

Number of eligible persons between 18 and 21 = 8% of x.

Number of persons between 18 and 21, who voted = 85% of (8% of x)(85100∗8100∗x)=681000x.

∴ Required percentage = (68×1000∗1x∗100)%=6.8%.

- In an election a candidate who gets 84% of the votes is elected by a majority of 476 votes What is the total number of votes polled ?

A. | 672 | |

B. | 700 | |

C. | 749 | |

D. | 849 |

**Answer & Explanation**

**Answer: **Option **B**

**Explanation:**

Let the total number of votes polled be x.

Then, votes polled by other candidate = (100 – 84)% of x = 16% of x.

∴84% of x – 16% of x = 476

<=> 68100x=476

<=> x=(476∗10068)=700.

- In an election between two candidates, one got 55% of theUotal valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :

A. | 2700 | |

B. | 2900 | |

C. | 3000 | |

D. | 3100 |

**Answer & Explanation**

**Answer: **Option **A**

**Explanation:**

Number of valid votes = 80%of 7500 = 6000.

Valid votes polled by other candidate = 45% of 6000 = (45100∗6000)= 2700.

- 10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters list was :

A. | 25000 | |

B. | 33000 | |

C. | 35000 | |

D. | 40000 |

**Answer & Explanation**

**Answer: **Option **C**

**Explanation:**

Let the total number of voters be x. Then, Votes polled = 90% of x.

Valid votes = 90% of (90% of x).

∴54% of [90% of (90% of x)] – 46% of [90% of (90% of x)] = 1620

<=> 8% of [90% of (90% of x)] = 1620

<=> 8100∗90100∗90100∗x=1620

<=> x=(1620∗100∗100∗1008∗90∗90)=25000.

- At an election involving two candidates, 68 votes were declared invalid. The winning candidate secures 52% and wins by 98 votes. The total number of votes polled is :

A. | 2382 | |

B. | 2450 | |

C. | 2518 | |

D. | None of these. |

**Answer & Explanation**

**Answer: **Option **C**

**Explanation:**

Let the number of valid votes be x.

Then, 52% of x – 48% of x = 98 <=> 4% of x = 98

<=> 4100x=98

<=> x = 98 * 25 = 2450.

∴ Total number of votes polled = (2450 + 68) = 2518.

- In an election, 30% of the voters voted for candidate A whereas 60% of the remaining voted for candidate B. The remaining voters did not vote. If the difference between those who voted for candidate A and those who did not vote was 1200, how many individuals were eligible for casting vote in that election ?

A. | 10, 000 | |

B. | 45, 000 | |

C. | 60, 000 | |

D. | 72, 000 |

**Answer & Explanation**

**Answer: **Option **C**

**Explanation:**

Let the number of persons eligible to vote be x.

Then, voters who voted for A = 30% of x.

Voters who voted for B = 60% of (70% of x).= (60100∗70100∗100)%of x = 42% of x.

Voters who did not vote = [100 – (30 + 42)]% of x = 28% of x.

∴30% of x – 28% of x= 1200

<=> 2% of x= 1200

<=> x = (1200∗1002)=60000.

- A student secures 90%, 60% and 54% marks in test papers with 100, 150 and 200 respectively as maximum marks.The percentage of his aggregate is :

A. | 64 | |

B. | 68 | |

C. | 70 | |

D. | None of these. |

**Answer & Explanation**

**Answer: **Option **A**

**Explanation:**

Total marks secured = (90% of 100 + 60% of 150 + 54% of 200) (90100∗100+60100∗150+54100∗200)=(90+90+108)=288.

Total maximum marks = (100 + 150 + 200) = 450.

∴

Aggregate percentage = (288450∗100)%=64%.

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