# 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 bank agrees to lend a loan to Arvind of Rs. 2,38,75,697 which falls short by 17% for starting his business. How much more loan would he need?

 A) 4890203 B) 4375303 C) 5700108 D) 5125533

Explanation:

15 323
Q:

18% of 60 is 54% of __.

 A) 40 B) 30 C) 20 D) 180

Explanation:

5 312
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) Rs.440 B) Rs.425 C) Rs.450 D) Rs.475

Explanation:

0 302
Q:

A has thrice as much amount as that of B and B has 40% more amount than C. If the average of the amount of all three of them is Rs 1320, then what amount (in Rs) A has?

 A) 2410 B) 2520 C) 2250 D) 3240

Explanation:

5 300
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:

3 297
Q:

An electric bulb was bought at Rs. 4200. Its value depriciates at the rate of 8% per annum. Its value after one year will be

 A) Rs. 3684 B) Rs. 3800 C) Rs. 3864 D) Rs. 3746

Explanation:

0 288
Q:

The income of P is 50% more than Q’s income and the income of Q is 50% more than R’s income. P’s income is how much percentage more than R’s income?

 A) 225 B) 150 C) 125 D) 100

Explanation:

3 261
Q:

The value of a car depreciates at the rate of 15% per annum. If its present value is Rs 433500, then what was the value (in Rs) of the car 2 years ago?

 A) 594200 B) 620000 C) 563550 D) 600000