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.

225 66022
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 .

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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 =

253 64497
Q:

405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child recieve ?

 A) 9 B) 10 C) 11 D) 12

Explanation:

Let the total number of children be x.

Then, x * (20% of x) = 405

=> x * 20x/100 = 405

$15x2$ = 405

=> x=45

Number of sweets received by each child = 20% of 45 = 9.

291 60237
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.

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Q:

In an election only two candidates contested 20% of the voters did not vote and 120 votes were declared as invalid. The winner got 200 votes more than his opponent  thus he secured 41% votes of the total voters on the voter list. Percentage votes of the defeated candidate out of the total votes casted is:

 A) 47.5% B) 41% C) 38% D) 45%

Explanation:

Let there be x voters and k votes goes to loser then

0.8x - 120 = k + (k + 200)

k+200 = 0.41x

=> k = 1440

and  (k + 200) =1640

Therefore  1440/3200 x 100 = 45%

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Q:

A number is decreased by 10% and then increased by 10%.  The number so obtained is 10 less than the original number. What was the oiginal number ?

 A) 1000 B) 2000 C) 3000 D) 4000

Explanation:

Let the original number be x.

Final number obtained = 110% of (90% of x) =(110/100 * 90/100 * x) = (99/100)x.

x-(99/100)x=10

=> x =1000

145 48712
Q:

If A's height is 40% less than that of B, how much percent B's height is more than that of A?

 A) 66.66% B) 76.66% C) 96.66% D) 86.66%