# 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's salary is 40% of B's salary which is 25% of C's salary. What percentage of C's salary is A's salary ?

 A) 10 B) 20 C) 30 D) 40

Explanation:

A's Salary  = 40% of B = 40% of (25% of C) = 40/100[(52/100)*100] % of C = 10% of C.

308 86527
Q:

If 75% of a number is added to 75, then the result is the number itself. The number is :

 A) 100 B) 200 C) 300 D) 400

Explanation:

Let the number be x, Then

75% of x + 75 = x

=> x - 75x/100 =75

=> x =  300 .

353 85895
Q:

25% of 25% Is Equal To

 A) 0.0625 B) 0.0210 C) 0.03145 D) 0.3210

Explanation:

25% of 25% means

25/100 of 25/100

i.e, 1/4 of 1/4

or in other words 1/4 x 1/4=1/16

Hence, the answer is 1/16 = 0.0625.

88 81192
Q:

A salesman gets commission on total sales at 9%. If the sale is exceeded Rs.10,000 he gets an additional commission as bonus of 3% on the excess of sales over Rs.10,000. If he gets total commission of Rs.1380, then the bonus he received is:

 A) Rs.180 B) Rs.120 C) Rs.480 D) data insufficient

Explanation:

Commission up to 10000 = $10000x9100$ = 900

Again after 10000,

Commission    :   Bonus

9       :   3

3x        :   x

Therefore,   Bonus =

342 77313
Q:

56% of 225 + 20% of 150 = ? - 109

Find the value of '?' in the above equation

 A) 264 B) 220 C) 241 D) None

Explanation:

Given 56% of 225 + 20% of 150 = ? - 109

we know that a% of b = b% of a

Now,

225% of 56 + 20% of 150 = ? - 109

200% of 56 + 25% of 56 + 20% of 150 = ? - 109

112 + 14 + 30 = ? - 109

? = 112 + 14 + 30 + 109

? = 264

57 72162
Q:

45% of 750  -  25% of 480 = ?

 A) 337.50 B) 217.50 C) 376.21 D) 120

Explanation:

Given expression = (45 x 750/100) - (25 x 480/100) = (337.50 - 120) = 217.50

71 69523
Q:

Gaurav spends 30% of his monthly income on food articles, 40% of the remaining on conveyance and clothes and saves 50% of the remaining. If his monthly salary is Rs. 18,400, how much money does he save every month ?

 A) 3864 B) 4903 C) 5849 D) 6789

Explanation:

Saving  = 50% of (100 - 40)% of (100 - 30)% of Rs. 18,400 = Rs. (50/100 * 60/100 * 70/100 * 18400) = Rs. 3864.

324 68629
Q:

A housewife saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction ?

 A) 8 B) 9 C) 10 D) 11

Explanation:

Actual price = Rs. (25 + 2.50) = Rs. 27.50.

Saving = 2.50

Percentage Saving = [(2.50/27.50)*100]

= 2500/275

$9111$%

$≈9$%