# 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:

What percent of 7.2 kg is 18 gms ?

 A) .25% B) .5% C) .75% D) 1%

Explanation:

Required percentage = (18/7200 * 100)% =  1/4% = 0.25%

192 47119
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

$9111$%

$≈9$%

108 44533
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.

50 39537
Q:

270 candidates appeared for an examination, of which 252 passed. The pass percentage is :

 A) (91 + 1/3)% B) (93 + 1/3 )% C) (97 + 1/3 )% D) (98 + 1/3) %

Explanation:

Pass percentage  =[(252/270)*100] % =280/3 % =$9313$ 9 %

111 37703
Q:

The ratio 5 : 4 expressed as a percent equals :

 A) 12.5 % B) 40 % C) 80 % D) 125 %

Explanation:

5 : 4 = 5/4 = ( (5/4) x 100 )% = 125%.

155 37288
Q:

Ram sell his goods 25% cheaper than Shyam and 25% dearer than Bram. How much % is Bram's good cheaper than Shyam ?

 A) 60% B) 40% C) 50% D) 30%

Explanation:

Lets say shyam sells at 100,

Since Ram sells 25% cheaper than Shyam,

Therefor Ram sells at less than 25% of100 or 75 rs.

Ram sells 25% dearer than Bram or 125% of Ram =100% of Bram or

125% of x (say x price of bram )=75rs.
or 100% of x =60rs.
hence price of bram is 60rs.

now Bram's good is cheaper than Shyam's as (100-60)x100/100% or 40%.

Hence Brams Good is 40% cheaper than that of Shyam's good.

77 34647
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

43 34522
Q:

If the pice of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumpion of sugar by

 A) 15 B) 20 C) 25 D) 30