1. Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first

A. 8% B. 9% C. 10% D. 11%

Answer: Option C
Explanation: Let the third number is x. then first number = (100-30)% of x = 70% of x = [latex]\frac{7x}{10}[/latex] The second number is ([latex]\frac{63x}{100}[/latex]) Difference = [latex]\frac{7x}{10}[/latex] - [latex]\frac{63x}{100}[/latex] = [latex]\frac{7x}{10}[/latex] So the required percentage is, the difference is what percent of the first number => ([latex]\frac{7x}{100}[/latex] * [latex]\frac{10}{7x}[/latex])% = 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.

A. 40% B. 42% C. 44% D. 46%

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 ?

A. 75 B. 100 C. 125 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.

A. 60 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

A. 1.5 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 * [latex]\frac{20}{100}[/latex] = 1.6

6. Raman's salary was decreased by 50% and subsequently increased by 50%. How much percent does he loss.

A. 75 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.

A. z = x B. 2z = x C. z = 2x D. None of above

Answer: Option C
Explanation: It is , y% of z = 2(x% of y) => [latex]\frac{YZ}{100}[/latex] = [latex]\frac{2XY}{100}[/latex] => z = 2x
8. If 15% of 40 is greater than 25% of a number by 2, the number is

A. 14 B. 16 C. 18 D. 20

Answer: Option B
Explanation: [latex]\frac{15}{100}[/latex] * 40 - [latex]\frac{25}{100}[/latex] * x = 2 or [latex]\frac{X}{4}[/latex] = 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.

A. 40% 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. => [latex]\frac{60}{120}[/latex]* 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

A. 55% B. 56% C. 57% D. 58%

Answer: Option C
Explanation: Total number of votes polled = (1136 + 7636 + 11628) = 20400 So, Required percentage = [latex]\frac{11628}{20400}[/latex]* 100 = 57%

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. 42,30 B. 42,31 C. 42,32 D. 42,33

Answer: Option D
Explanation: Let their marks be (x+9) and x. Then, x+9 = [latex]\frac{56}{100}[/latex](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

A. 140 B. 150 C. 180 D. 200

Answer: Option C
Explanation: ([latex]\frac{1}{4}[/latex]) * ([latex]\frac{1}{3}[/latex]) * ([latex]\frac{2}{5}[/latex]) * 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

A. 5 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

A. 5500 B. 6000 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 => [latex]\frac{75}{100}[/latex] * [latex]\frac{90}{100}[/latex] * x = 4050 => x = [latex]\frac{(4050*50)}{27}[/latex] = 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

A. 10 B. 20 C. 30 D. 40

Answer: Option A
Explanation: Clue: Answer will be 5% of 1000 - 4% of 1000