# 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:

42% of an alloy was silver. If in a quantity of alloy there was 147 g of silver, what was the quantity of the other elements in the alloy?

 A) 261 g B) 203 g C) 273 g D) 350 g

Explanation:

2 842
Q:

Samar was given some money to take care of his travel during an 8-day sales drive he had to undertake. However he had to increase his stay by another 6 days and as a result his average daily travel allowance went down by Rs. 120. What was the amount that was sanctioned to him in the beginning?

 A) ₹ 560 B) ₹ 840 C) ₹ 1120 D) ₹ 2240

Explanation:

3 838
Q:

If the selling price of an article is 8% more than the cost price and the discount offered is 10% on the marked price of the article, then what is the ratio of the cost price to the marked price?

 A) 5 : 6 B) 8 : 9 C) 3 : 4 D) 4 : 5

Explanation:

9 835
Q:

A small scale business has the following expenses: procurement (25%), employees' salary (25%) and 50% for maintenance.

If the business pays a total salary of Rs. 2,00,000 then what is its maintenance expense?

 A) ₹ 3,00,000 B) ₹ 2,00,000 C) ₹ 2,50,000 D) ₹ 4,00,000

Explanation:

1 832
Q:

A runner is running at a speed of 40 kim/h. If he runs at a speed of 30 km/h, then what will the decrease in the percentage of his speed be?

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

Explanation:

4 831
Q:

Raghav spends 80% of his income. If his income increases by 12% and his expenditure increases by 17.5%, then what is the percentage decrease in his savings?

 A) 12% B) 10% C) 8% D) 15%

Explanation:

3 823
Q:

Rahul’s salary is 50% more than Rohit’s salary. If Rahul saves Rs 2250 which is 8% of his salary, then what is Rohit’s salary (in Rs)?

 A) 22250 B) 24450 C) 26350 D) 18750

Explanation:

1 821
Q:

56% of 375 is:

 A) 210 B) 196 C) 224 D) 168