**Example**: 10% = \(\frac{10}{100}\) = \(\frac{1}{10}\)

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**Answer**: Option C

**Explanation**:

Let the third number is x.

then first number = (100-30)% of x

= 70% of x = \(\frac{7x}{10}\)

The second number is (\(\frac{63x}{100}\))

Difference = \(\frac{7x}{10}\) – \(\frac{63x}{100}\) = \(\frac{7x}{10}\)

So the required percentage is, the difference is what percent of the first number

=> (\(\frac{7x}{100}\) * \(\frac{10}{7x}\))% = 10%

**2. In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then find the percentage of students who passed in both the subjects.**

**Answer**: Option C

Failed in mathematics, n(A) = 34

Failed in English, n(B) = 42

n(A∪B) = n(A) + n(B) − n(A∩B) = 34 + 42 − 20 = 56 Failed in either or both subjects are 56Percentage passed = (100 − 56)% = 44%

**3. Out of 450 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?**

**D. ** 150

**Answer**: Option B

**Explanation**:

Students who play cricket, n(A) = 325

Students who play football, n(B) = 175

Total students who play either or both games,

= n(A∪B) = 450 − 50 = 400Required Number, n(A∩B) = n(A) + n(B) − n(A∪B) = 325 + 175 − 400 = 100

**4. The teacher took the exam for English, the average for the entire class was 80 marks. If we say that 10% of the students scored 95 marks and 20% scored 90 marks then calculate average marks of the remaining students of the class.**

**B.** 70

**C.** 75

**D. ** 80

**Answer**: Option C

**Explanation**:

Lets assume that total number of students in class is 100 and required average be x.

Then from the given statement we can calculate :

(10 * 95) + (20 * 90) + (70 * x) = (100 * 80)

=> 70x = 8000 – (950 + 1800) = 5250

=> x = 75.

**5. How many liters of pure acid are there in 8 liters of a 20% solution**

**B.** 1.6

**C.** 1.7

**D. ** 1.8

**Answer**: Option B

**Explanation**:

Question of this type looks a bit typical, but it is too simple, as below…

It will be 8 * \(\frac{20}{100}\) = 1.6

**B.** 65

**C.** 45

**D. ** 25

**Answer**: Option D

**Explanation**:

Let the origianl salary = Rs. 100

It will be 150% of (50% of 100)

= (150/100) * (50/100) * 100 = 75

So New salary is 75, It means his loss is 25%

**7. If x% of y is 100 and y% of z is 200, then find the relation between x and z.**

**B.** 2z = x

**C.** z = 2x

**D. ** None of above

**Answer**: Option C

**Explanation**:

It is , y% of z = 2(x% of y)

=> \(\frac{YZ}{100}\) = \(\frac{2XY}{100}\)

=> z = 2x

**8. If 15% of 40 is greater than 25% of a number by 2, the number is**

**B.** 16

**C.** 18

**D. ** 20

**Answer**: Option B

**Explanation**:

\(\frac{15}{100}\) * 40 – \(\frac{25}{100}\) * x = 2 or \(\frac{X}{4}\) = 4 so x = 16

**9. A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets.**

**B.** 50%

**C.** 60%

**D. ** 70%

**Answer**: Option B

**Explanation**:

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

= 120 – (60)

= 60

Now, we need to calculate 60 is what percent of 120.

=> \(\frac{60}{120}\)* 100 = 50 %

**10. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get **

**B.** 56%

**C.** 57%

**D. ** 58%

**Answer**: Option C

**Explanation**:

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

So, Required percentage = \(\frac{11628}{20400}\)* 100 = 57%

**D. ** 42,33

**Answer**: Option D

**Explanation**:

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

Then, x+9 = \(\frac{56}{100}\)(x + 9 +x)

=> 25(x + 9)

=> 14 (2x + 9)

=> 3x = 99

=> x = 33.

So, their marks are 42 and 33

**12. One-fourth of one-third of two-fifth of a number is 15. What will be40% of that number**

**B.** 150

**C.** 180

**D. ** 200

**Answer**: Option C

**Explanation**:

(\(\frac{1}{4}\)) * (\(\frac{1}{3}\)) * (\(\frac{2}{5}\)) * x = 15 then x = 15 * 30 = 450

40% of 450 = 180

**13. Rahul’s Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems. Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly, still he got less than 60% problems right. How many more questions he would have to answer more to get passed**

**B.** 6

**C.** 7

**D. ** 8

**Answer**: Option A

**Explanation**:

Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)

= 7 + 12 + 21 = 40.

Questions to be answered correctly for 60% = 60% of total quations

= 60 % of 75 = 45.

He would have to answer 45 – 40 = 5

**14. 10% of inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the original inhabitants**

**C.** 6500

**D. ** 7000

**Answer**: Option B

**Explanation**:

Let the total number is x,

then,

(100-25)% of (100 – 10)% x = 4050

=> 75% of 90% of x = 4050

=> \(\frac{75}{100}\) * \(\frac{90}{100}\) * x = 4050

=> x = \(\frac{(4050*50)}{27}\) = 6000

**15. If a sales tax is reduced from 5% to 4%, then what difference it will make if you purchase an item of Rs. 1000**

**B.** 20

**C.** 30

**D. ** 40

**Answer**: Option A

**Explanation**:

Clue: Answer will be 5% of 1000 – 4% of 1000