 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  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)  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  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)
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?  
Answer: Option B
Explanation:
Number of runs made by running = 110  (3 x 4 + 8 x 6)
= 110  (60)
= 50.

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:
 
Answer: Option C
Explanation:
Let their marks be (x + 9) and x.
25(x + 9) = 14(2x + 9)
3x = 99
x = 33
So, their marks are 42 and 33.

3. 
A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
 
Answer: Option D
Explanation:
Suppose originally he had x apples.
Then, (100  40)% of x = 420.

4. 
What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
 
Answer: Option C
Explanation:
Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14

5. 
If A = x% of y and B = y% of x, then which of the following is true?
 
Answer: Option E
Explanation:
A = B.

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