# Percentage

Q21. If the price of pencil is reduced by 20%, a person can buy 2 more pencils for a rupee. How many pencils are available for a rupee ?

(a) 5

(b) 8

(c) 12

(d) 18

**Answer:** (b) 8

Let no. of pencils be available for a rupee be n

Reduced Price = (80/100) X 1 = Rs. 4/5

4/5 rupee fetch n pencils

∴ 1 rupee fetch = n X (5/4) pencil

∴ 5n/4 = n+2

⇒ 5n = 4n + 8

⇒ n = 8

Q22. A number is first increased by 40% and then reduced by 40%. What would be the percentage change in the number ?

(a) 12%

(b) 16%

(c) 19%

(d) 21%

**Answer:** (b) 16%

Let the number be 100

∴ Final Value = 60% of 140% of 100 = (60/100) X (140/100) X 100 = 84

Change = 16% decrease

Q23. How is ½% expressed as a decimal fraction ?

(a) 0.005

(b) 0.010

(c) 0.015

(d) 0.050

**Answer:** (a) 0.005

½% = ½/100 = 1/200 = 0.005

Q24. y% of y is the same as 10% of

(a) y/10

(b) y^{2}/10

(c) y/100

(d) y^{2}/100

**Answer:** (b) y^{2}/10

Let, the required number be a

A/Q y% of y = 10% of a

⇒ (y/100) X y = (10/100) X a

⇒ y^{2} = 10a

⇒ a = y^{2}/10

Q25. 12% of 980 - ? % of 450 = 30% of 225

(a) 103/17

(b) 111/15

(c) 117/17

(d) 167/15

**Answer:** (d) 167/15

Let, the required number be x

A/Q 12% of 980 - ? % of 450 = 30% of 225

⇒ (12/100) X 980 - (x/100) X 450 = (30/100) X 225

⇒ 11760 - 450x = 6750

⇒ 450x = 5010

⇒ x = 167/15

Q26. 20% of a number is less than 15% of 550 by 10. The number is

(a) 215/2

(b) 577/2

(c) 807/2

(d) 925/2

**Answer:** (d) 925/2

Let, the required number be x

A/Q 20% X x = 15% of 550 + 10

⇒ | 20x | = | 15 | X 550 + 10 |

100 | 100 |

⇒ | x | = | 165 | + 10 |

5 | 2 |

⇒ x = 5 ( | 165 + 20 | ) |

2 |

⇒ x = 5 X (185/2) = 925/2

Q27. Two numbers are less than a third number by 30% and 37% respectively. How much percent is the second number less than the first ?

(a) 10%

(b) 20%

(c) 35%

(d) 40%

**Answer:** (a) 10%

Let, the 3rd number be x

∴ 1st number = x - (30x/100) = 70x/100

2nd number = x - (37x/100) = 63x/100

1st number - 2nd number = | 70x | - | 63x | = | 7x |

100 | 100 | 100 |

Required % = | 7x/100 | X 100 = | 7x | X 100 = 10% |

70x/100 | 70x |

Q28. How is 2/5 expressed as percentage ?

(a) 20%

(b) 30%

(c) 40%

(d) 50%

**Answer:** (c) 40%

Required percentage = (2/5) X 100% = 40%

Q29. Out of an earning of Rs. 800 a man spends 60%. How much does he save ?

(a) Rs. 140

(b) Rs. 270

(c) Rs. 320

(d) Rs. 410

**Answer:** (c) Rs. 320

Speed = 60%

∴ Save = 40%

Required amount = Rs. 800 X 40% = Rs. 800 X (40/100) = Rs. 320

Q30. 10% of the voters in an election did not cast their votes. In the election, there were only two candidates. The winner by obtaining 50% of the total votes defeated his contestent by 1100 votes. The total number of voters in the election was.

(a) 5000

(b) 6500

(c) 8000

(d) 11000

**Answer:** (d) 11000

Let, the total number of voters be x

Votes cast = 90% of x = (90/100) X x = 9x/10

Votes in favour of winning candidates = 50% of x = (50/100) X x = x/2

Votes polled by defeated candidates = (9x/10) - (x/2) = (9x-5x)/10 = 2x/5

A/Q | x | - | 2x | = 1100 |

2 | 5 |

⇒ | 5x - 4x | = 1100 |

10 |

⇒ x = 1100 X 10 = 11000

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