**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

To express a/b as a percent: We have, a/b = (a/b x 100)

Thus, 1/4 = (1/4 x 100)% = 25%.

**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/ (100 + R) x 100]%

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

decrease the expenditure is:

[R/(100 – R) x 100]%

**Results on Population:**

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

then:

Population after n years = P (1 + R/100)n

Population n years ago = (P/ 1 + R/100)n

**Results on Depreciation:**

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

Then:

Value of the machine after n years = P (1 – R/100)n

Value of the machine n years ago = P/( 1 – R/100)n

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

If A is R% less than B, then B is more than A by [R/(100 – R) x 100]%.

**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%

**Answer: Option B**

Explanation:

Number of runs made by running = 110 – (3 x 4 + 8 x 6)

= 110 – (60)

= 50.

Required percentage = (50/110 x 100)% = 45 5/11%

**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

**Answer: Option C**

Explanation:

Let their marks be (x + 9) and x.

Then, x + 9 = 56/100 (x + 9 + x)

25(x + 9) = 14(2x + 9)

3x = 99

x = 33

So, their marks are 42 and 33.

**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

**Answer: Option D**

Suppose originally he had x apples.

Then, (100 – 40)% of x = 420.

60/100 x X = 420

x =(420 x 100/60) = 700.

**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

**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

Required percentage = (14/70 x 100)% = 20%.

**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

**Answer: Option E**

Explanation:

x% of y = (x/100 x y) = (y/100 X x) = y% of x

A = B.

**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

**Answer: Option A**

Explanation:

20% of a = b=> 20 a = b.

b% of 20 = (b/100 x 20) = (20/100a x 1/100 x 20) = 4/100a = 4% of a.

** 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

**Answer: Option E**

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 + 2/3 of 48

80/100 x = 80

x = 100.

** 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

**Answer: Option D**

Explanation:

5% of A + 4% of B = 2/3 (6% of A + 8% of B)

5/100 A + 4/100 B = 2/3 (6/100 A + 8/100 B)

1/20A + 1/25B = 1/25A + 4/75 B

(1/20 – 1/25) A =(4/75 – 1/25)B

1/100A = 1/75B

A/B = 100/75 = 4/34

Required ratio = 4 : 3

**A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?**

A. 34%

B. 44%

C. 54%

D. 64%

**Answer: Option D**

Explanation:

Let the number be x.

Then, error = 5/3x – 3/5x = 16/15x.

Error% = (16/15x X 3/5x X 100)% = 64%.

**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

**Answer: Option A**

Explanation:

Number of valid votes = 80% of 7500 = 6000. Valid votes polled by other candidate = 45% of 6000

45/100 x 6000 = 2700.

**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%

**Answer: Option A**

Explanation:

Total number of votes polled = (1136 + 7636 + 11628) = 20400.

Required percentage = (11628/20400 x 100)% = 57%.

**Two tailor’s 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

**Answer: Option B**

Explanation:

Let the sum paid to Y per week be Rs. z.

Then, z + 120% of z = 550.

z + 120/100z = 550

11/5z = 550

z = (550 x 5/11) = 250.

**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

**Answer: Option C**

Explanation:

Let the amount taxable purchases be Rs. x.

Then, 6% of x = (30/100 x 100/6) = 5.

Cost of tax free items = Rs. [25 – (5 + 0.30)] = Rs. 19.70

**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

**Answer: Option A**

Explanation:

Rebate = 6% of Rs. 6650 = Rs. (6/100 x 6650) = Rs. 399.

Sales tax = 10% of Rs. (6650 – 399) = Rs. (10/100 x 6251) = Rs. 625.10

100

Final amount = Rs. (6251 + 625.10) = Rs. 6876.10

**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%

Answer: Option B

Explanation:

Increase in 10 years = (262500 – 175000) = 87500.

Increase% = (87500/ 175000 x 100)% = 50%.

Required average = (50/10)% = 5%.

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