# 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:

A boy has 120 balls of which some are white and the remaining are black. If the percentage of white balls is 45%, find the number of black balls he has.

 A) 56 B) 66 C) 64 D) 54

Explanation:

2 728
Q:

The price of sugaris increased by 20%. By what percentage must one cut down on the consumption of sugar, so that no extra amount has to be incurred on sugar?

 A) 1623°° B) 20°° C) 80°° D) 8313°°

Explanation:

3 727
Q:

A shopkeeper fixes the price of an article in such a way that after allowing 32% discount, he wants again of 14%. If the marked price is ₹342, then the cost price of the article is:

 A) ₹212 B) ₹204 C) ₹218 D) ₹196

Explanation:

1 717
Q:

Amir gave two successive discounts of 10% and 20% on a pencil. If the marked price of the pencil is Rs 3200, then what is the total value (in Rs) of the two discounts together?

 A) 940 B) 1086 C) 896 D) 1120

Explanation:

1 713
Q:

What is the difference between a single discount of 30% and a single discount equivalent to two successive discounts of 25% and 5%, being given on shopping of ₹2,000?

 A) ₹20 B) ₹25 C) No difference D) ₹15

Explanation:

0 701
Q:

In a test, Chandran secured 16 out of 45 marks. He will take another test and to pass he needs to secure an overall 48% marks. If the second test was out of 80, and he just passed, what was his percentage  marks in the second test?

 A) 48 B) 60 C) 44 D) 55

Explanation:

2 694
Q:

In a village, 15% of the population are females and there are 272 males. Find the total population of that village.

 A) 400 B) 420 C) 380 D) 320

Explanation:

0 683
Q:

An item is sold at two successive discounts of 10% and 10%. The selling price of article after the two discount is Rs 4050. If it is sold only at one discount of 20%, then
what will be the selling price (in Rs) of the article?

 A) 4000 B) 5000 C) 4500 D) 5500