ALL CONCEPT OF PERCENTAGE IN ONE GO

1.    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	=	1	.
	100		5

To express	a	as a percent: We have,	a	=		a	x 100	%.
	b		b			b

Thus,	1	=		1	x 100	%	= 25%.
	4			4

2.    Percentage Increase/Decrease:

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

	R	x 100	%
	(100 + R)

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

	R	x 100	%
	(100 - R)

3.    Results on Population:

Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:

1. Population after n years = P		1 +	R		n
			100

2. Population n years ago =	P
	1 + R n 100

4.    Results on Depreciation:

Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:

1. Value of the machine after n years = P		1 -	R		n
			100

2. Value of the machine n years ago =	P
	1 - R n 100

3. If A is R% more than B, then B is less than A by		R	x 100	%.
		(100 + R)

4. If A is R% less than B, then B is more than A by		R	x 100	%.
		(100 - R)

Q1:- A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?

A. 45% B. 45 5 % 11 C. 54 6 % 11 D. 55% Explanation: Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 110 - (60) = 50.  Required percentage = 50 x 100 % = 45 5 % 110 11

Q2-Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

A. 39, 30 B. 41, 32 C. 42, 33 D. 43, 34 Explanation: Let their marks be (x + 9) and x. Then, x + 9 = 56 (x + 9 + x) 100  25(x + 9) = 14(2x + 9)  3x = 99  x = 33 So, their marks are 42 and 33. Q3- In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is  of the number of students of 8 years of age which is 48. What is the total number of students in the school? A. 72 B. 80 C. 120 D. 150 E. 100 Explanation: Let the number of students be x. Then, Number of students above 8 years of age = (100 - 20) % of x = 80% of x. 80% of x = 48 + 2 of 48 3 80 x = 80 100  x = 100.

Q4-In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

A. 2700 B. 2900 C. 3000 D. 3100 Explanation: Number of valid votes = 80% of 7500 = 6000. Valid votes polled by other candidate = 45% of 6000 = 45 x 6000 = 2700. 100

Q5-Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?

A. Rs. 200 B. Rs. 250 C. Rs. 300 D. None of these Explanation: Let the sum paid to Y per week be Rs. z. Then, z + 120% of z = 550.  z + 120 z = 550 100 11 z = 550 5  z = 550 x 5   = 250. 11