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## Arithmetic: Percentage Test -4

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Question 1 |

Atish saves 20% of his salary. His salary has increased by 20% and his expenditure has increased by 30%. What is the percentage change in his savings?

A | 20% fall |

B | 4% fall |

C | 20% rise |

D | 4% rise |

Question 1 Explanation:

Let A be the income.

Expenditure = 0.8 A

Savings = 0.2 A => 20%

New income = 1.2 A (since 20% rise)

New expenditure = (0.8 A) X 1.3 (Since 30% rise) = 1.04A

So, new savings = 1.2A – 1.04A = 0.16A => 16%

% decrease = (20-16)/20 X 100 = 20%.

Expenditure = 0.8 A

Savings = 0.2 A => 20%

New income = 1.2 A (since 20% rise)

New expenditure = (0.8 A) X 1.3 (Since 30% rise) = 1.04A

So, new savings = 1.2A – 1.04A = 0.16A => 16%

% decrease = (20-16)/20 X 100 = 20%.

Question 2 |

The price of mangoes has increased by 25%. By what percent the consumption needs to be reduced so that the expense on mangoes remains the same?

A | 25% |

B | 33.33% |

C | 20% |

D | None |

Question 2 Explanation:

We solve this question using the principle of constancy.

Let original price = P

Increased Price- 1.25P

Original Consumption= C

Increased Consumption= I

It is given that expense is the same, that is:

1.25 x I = P x C

I=0.8 C

% decrease = {(1-0.8)/1} X 100 = 20%

Let original price = P

Increased Price- 1.25P

Original Consumption= C

Increased Consumption= I

It is given that expense is the same, that is:

1.25 x I = P x C

I=0.8 C

% decrease = {(1-0.8)/1} X 100 = 20%

Question 3 |

The side of a square is increased by 20%. The percentage change in its area is ___

A | 20% |

B | 44% |

C | 36% |

D | 400% |

Question 3 Explanation:

Area of a square: side x side

% change in area = 1.2 X 1.2 (since area = side X side) = 1.44

= 44%.

% change in area = 1.2 X 1.2 (since area = side X side) = 1.44

= 44%.

Question 4 |

If the length of a rectangle is increased by 33.33%, by what percentage should the breadth be reduced to make the area same?

A | 20% |

B | 33.33% |

C | 25% |

D | None |

Question 4 Explanation:

Area of original rectangle: L X B

Area of new rectangle: 1.33L x b

Since the areas are the same:

1.33 L x b = L x B

b = ¾ B

Decrease in breadth: 25%

Area of new rectangle: 1.33L x b

Since the areas are the same:

1.33 L x b = L x B

b = ¾ B

Decrease in breadth: 25%

Question 5 |

10. In the 2013 Lok Sabha Election, two candidates, X and Y, contested from Delhi. A secured 64% of the votes and won 84000 votes. Find the total number of votes if 20% of votes polled were invalid.

A | 300000 |

B | 375000 |

C | 350000 |

D | 400000 |

Question 5 Explanation:

X got 64% of the Valid Votes, V

Y got 36% of the Valid Votes, V

Difference: 28% of V = 84000

Therefore, V = 300000

Only 80% of the total votes are valid.

Therefore total votes = 300000 * (100/80) = 375000

Y got 36% of the Valid Votes, V

Difference: 28% of V = 84000

Therefore, V = 300000

Only 80% of the total votes are valid.

Therefore total votes = 300000 * (100/80) = 375000

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