PERCENTAGES

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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)

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1.	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% View Answer Workspace Report Discuss in Forum

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2.	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 View Answer Workspace Report Discuss in Forum

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3.	A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
	A. 588 apples B. 600 apples C. 672 apples D. 700 apples View Answer Workspace Report Discuss in Forum

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4.	What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
	A. 1 B. 14 C. 20 D. 21 View Answer Workspace Report Discuss in Forum

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5.

If A = x% of y and B = y% of x, then which of the following is true?

A. A is smaller than B. B. A is greater than B C. Relationship between A and B cannot be determined. D. If x is smaller than y, then A is greater than B. E. None of these 6.  If 20% of a = b, then b% of 20 is the same as: A. 4% of a B. 5% of a C. 20% of a D. None of these View Answer Workspace Report Discuss in Forum 7.  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 View Answer Workspace Report Discuss in Forum 8.  Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B. A. 2 : 3 B. 1 : 1 C. 3 : 4 D. 4 : 3 View Answer Workspace Report Discuss in Forum 9.  A student multiplied a number by 3 instead of 5 . 5 3 What is the percentage error in the calculation? A. 34% B. 44% C. 54% D. 64% View Answer Workspace Report Discuss in Forum 10.  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 View Answer Workspace Report Discuss in Forum 1.  Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get? A. 57% B. 60% C. 65% D. 90% View Answer Workspace Report Discuss in Forum 12.  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 View Answer Workspace Report Discuss in Forum 13.  Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? A. Rs. 15 B. Rs. 15.70 C. Rs. 19.70 D. Rs. 20 View Answer Workspace Report Discuss in Forum 14.  Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods. A. Rs. 6876.10 B. Rs. 6999.20 C. Rs. 6654 D. Rs. 7000 View Answer Workspace Report Discuss in Forum 15.  The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is: A. 4.37% B. 5% C. 6% D. 8.75% View Answer Workspace Report Discuss in Forum

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