# Percentage Questions

**FACTS AND FORMULAE FOR PERCENTAGE QUESTIONS**

**I.Concept of Percentage :** By a certain percent , we mean that many hundredths. Thus x percent means x hundredths, written as x%.

**To express x% as a fraction : **We have , x% = x/100.

Thus, 20% = 20/100 = 1/5;

48% = 48/100 = 12/25, etc.

**To express a/b as a percent :** We have, % .

Thus, % = 25%;

**II.** If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is%

If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is%

**III. Results on Population : **Let the population of the town be P now and suppose it increases at the rate of R% per annum, then :

1. Population after n years =

2. Population n years ago =

**IV. Results on Depreciation :** Let the present value of a machine be P. Suppose it depreciates at the rate R% per annum. Then,

1. Value of the machine after n years =

2. Value of the machine n years ago =

**V.** If A is R% more than B, then B is less than A by

%

If A is R% less than B , then B is more than A by

%

A) 2500 | B) 2700 |

C) 2900 | D) 3100 |

Explanation:

Total number of votes = 7500

Given that 20% of Percentage votes were invalid

=> Valid votes = 80%

Total valid votes =

1st candidate got 55% of the total valid votes.

Hence the 2nd candidate should have got 45% of the total valid votes

=> Valid votes that 2nd candidate got = total valid votes x

A) 4% of a | B) 6% of a |

C) 8% of a | D) 10% of a |

A) 20 | B) 30 |

C) 40 | D) 50 |

Explanation:

The fruit content in both the fresh fruit and dry fruit is the same.

Given, fresh fruit has 68% water.so remaining 32% is fruit content. weight of fresh fruits is 100kg

Dry fruit has 20% water.so remaining 80% is fruit content.let weight if dry fruit be y kg.

fruit % in freshfruit = fruit% in dryfruit

(32/100) * 100 = (80/100 )* y

we get, y = 40 kg

A) 10000 | B) 12000 |

C) 14000 | D) 16000 |