# 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, $\frac{a}{b}=\left(\frac{a}{b}×100\right)%$ .

Thus, $\frac{1}{4}=\left(\frac{1}{4}×100\right)%=25%$

II. If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is $\left[\frac{R}{\left(100+R\right)}×100\right]%$

If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is $\left[\frac{R}{\left(100-R\right)}×100\right]%$

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 = $P{\left(1+\frac{R}{100}\right)}^{n}$

2. Population n years ago =  $\frac{P}{{\left(1+\frac{R}{100}\right)}^{n}}$

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 = $P{\left(1-\frac{R}{100}\right)}^{n}$

2. Value of the machine n years ago = $\frac{P}{{\left(1-\frac{R}{100}\right)}^{n}}$

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

$\left[\frac{R}{\left(100+R\right)}×100\right]%$

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

$\left[\frac{R}{\left(100-R\right)}×100\right]%$

Q:

You went to buy 3 articles worth Rs.500 each. However, as per the discount sale going on in the shop, you paid for two and got one free. What is the discount percentage in the deal?

 A) 30% B) 33% C) 33.13% D) 33.33%

Explanation:

3 403
Q:

Population of Patna city is 96,000, the decreasing rate of population is 800 per year. Population of Patliputra is 68,000, the increasing rate of population is 1200 per year. In how many years will the population of both places be equal?

 A) 10 B) 14 C) 18 D) 22

Explanation:

1 400
Q:

58% of 350 is

 A) 217 B) 203 C) 210 D) 196

Explanation:

0 395
Q:

The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget?

 A) 70% B) 80% C) 30% D) 20%

Explanation:

0 383
Q:

The difference between 66 % of a number and 44% of the same number is 275. What is the 64% of that number?

 A) 800 B) 840 C) 760 D) 600

Explanation:

0 373
Q:

Jane won a lottery and gets 1/3 of the winning amount and donates Rs.6000 which is 1/6, find how much the lottery was worth.

 A) 6000 B) 18000 C) 54000 D) 108000

Explanation:

1 370
Q:

The marked prices of big and small note books are Rs.10 and RS.15 respectively. A student bought 5 dozen small and 10 dozen big note books at a total discount of 5% Find the total discount amount.

 A) Rs.100 B) Rs.110 C) Rs.120 D) Rs.130

Explanation:

0 360
Q:

Inclusive of an 18% peak-time surcharge a taxi fare came to Rs. 531. What would the payable amount have been without the surcharge?

 A) ₹ 440 B) ₹ 425 C) ₹ 450 D)  ₹ 475