Mathematics Part 1

Question 1:

Topic: Arithmetic Aptitude

Question: If 4 times a number minus 5 equals 19, what is the number?

Options:

A. 4

B. 5

C. 6

D. 7

Correct Answer: C. 6

Explanation:

Let the number be x. According to the problem, 4x – 5 = 19. Solving for x gives 4x = 24, so x = 6.

 

Question 2:

Topic: Time and Speed

Question: If a cyclist covers 45 kilometers in 3 hours, what is their average speed?

Options:

A. 12 km/h

B. 15 km/h

C. 18 km/h

D. 20 km/h

Correct Answer: B. 15 km/h

Explanation:

Average speed = Total Distance / Total Time. Therefore, average speed = 45 km / 3 hours = 15 km/h.

 

Question 3:

Topic: Probability

Question: A box contains 2 yellow, 3 green, and 5 blue marbles. What is the probability of drawing a green marble?

Options:

A. 1/5

B. 3/10

C. 1/2

D. 3/5

Correct Answer: B. 3/10

Explanation:

There are 3 green marbles out of 10 total marbles. Therefore, the probability is 3/10.

 

Question 4:

Topic: Percentages

Question: If a person’s income increases by 20% to ₹36,000, what was their original income?

Options:

A. ₹28,000

B. ₹30,000

C. ₹32,000

D. ₹35,000

Correct Answer: B. ₹30,000

Explanation:

Let the original income be x. A 20% increase means the income becomes x + 20% of x. Therefore, x + 0.20x = ₹36,000. Solving for x gives x = ₹30,000.

 

Question 5:

Topic: Mensuration

Question: What is the area of a circle with a radius of 7 cm?

Options:

A. 44 cm²

B. 154 cm²

C. 196 cm²

D. 246 cm²

Correct Answer: B. 154 cm²

Explanation:

Area of a circle = πr², where r is the radius. So, area = π × 7² = 22/7 × 49 ≈ 154 cm².

 

Question 6:

Topic: Data Interpretation

Question: In a bar chart, the number of books sold by a store in January was 500, and in February it was 650. What is the percentage increase?

Options:

A. 25%

B. 30%

C. 35%

D. 40%

Correct Answer: B. 30%

Explanation:

The increase is 650 – 500 = 150. The percentage increase is (150/500) × 100 = 30%.

 

Question 7:

Topic: Pipes and Cisterns

Question: If one tap can fill a tank in 40 minutes, and another tap can fill the same tank in 60 minutes, how long will it take both taps to fill the tank together?

Options:

A. 24 minutes

B. 25 minutes

C. 30 minutes

D. 35 minutes

Correct Answer: A. 24 minutes

Explanation:

The first tap fills 1/40 and the second tap fills 1/60 of the tank per minute. Together, they fill 1/40 + 1/60 = 1/24 of the tank per minute. Therefore, it will take 24 minutes to fill the tank.

 

Question 8:

Topic: Profit and Loss

Question: A shopkeeper buys goods for ₹800 and sells them for ₹1,000. What is his profit percentage?

Options:

A. 20%

B. 25%

C. 30%

D. 35%

Correct Answer: B. 25%

Explanation:

Profit = Selling Price – Cost Price = ₹1,000 – ₹800 = ₹200. Profit Percentage = (Profit / Cost Price) × 100 = (₹200/₹800) × 100 = 25%.

 

Question 9:

Topic: Number Series

Question: What is the next number in the series: 3, 9, 27, 81, …?

Options:

A. 243

B. 162

C. 108

D. 324

Correct Answer: A. 243

Explanation:

The series is a geometric progression where each term is multiplied by 3. The next number is 81 × 3 = 243.

 

Question 10:

Topic: Arithmetic Aptitude

Question: If the product of two numbers is 48 and their sum is 14, what is the larger number?

Options:

A. 6

B. 8

C. 12

D. 14

Correct Answer: B. 8

Explanation:

Let the numbers be x and y. x × y = 48 and x + y = 14. Solving these equations, the larger number is 8.

 

Question 11:

Topic: Ratios and Proportions

Question: If the ratio of A’s and B’s ages is 4:3 and A is 24 years old, how old is B?

Options:

A. 16 years

B. 18 years

C. 20 years

D. 22 years

Correct Answer: B. 18 years

Explanation:

A’s age / B’s age = 4/3. Since A’s age is 24, B’s age is (3/4) × 24 = 18 years.

 

Question 12:

Topic: Simple Interest and Compound Interest

Question: If ₹5,000 is invested at a simple interest rate of 10% per annum, how much interest will be earned in 3 years?

Options:

A. ₹1,000

B. ₹1,250

C. ₹1,500

D. ₹1,750

Correct Answer: C. ₹1,500

Explanation:

Simple Interest = Principal × Rate × Time. So, interest = ₹5,000 × 10/100 × 3 = ₹1,500.

 

Question 13:

Topic: Mensuration

Question: What is the volume of a cube with an edge length of 5 cm?

Options:

A. 75 cm³

B. 100 cm³

C. 125 cm³

D. 150 cm³

Correct Answer: C. 125 cm³

Explanation:

Volume of a cube = side³. So, volume = 5³ = 125 cm³.

 

Question 14:

Topic: Data Interpretation

Question: In a line graph, if the revenue of a company in 2018 was ₹200,000 and in 2019 it was ₹250,000, what is the percentage increase?

Options:

A. 20%

B. 25%

C. 30%

D. 35%

Correct Answer: B. 25%

Explanation:

The increase in revenue is ₹250,000 – ₹200,000 = ₹50,000. The percentage increase is (₹50,000/₹200,000) × 100 = 25%.

 

Question 15:

Topic: Time and Speed

Question: If a train covers a distance of 150 km in 3 hours, what is its average speed?

Options:

A. 45 km/h

B. 50 km/h

C. 55 km/h

D. 60 km/h

Correct Answer: B. 50 km/h

Explanation:

Average speed = Total Distance / Total Time. Therefore, average speed = 150 km / 3 hours = 50 km/h.

 

Question 16:

Topic: Arithmetic Aptitude

Question: If the sum of two numbers is 16 and their difference is 4, what is the larger number?

Options:

A. 6

B. 8

C. 10

D. 12

Correct Answer: C. 10

Explanation:

Let the numbers be x and y with x > y. We have x + y = 16 and x – y = 4. Solving these equations, we find x = 10 and y = 6. The larger number is 10.

 

Question 17:

Topic: Percentages

Question: If a dress is marked at ₹1,200 and sold at a discount of 15%, what is the sale price?

Options:

A. ₹900

B. ₹960

C. ₹1,020

D. ₹1,080

Correct Answer: C. ₹1,020

Explanation:

A 15% discount on ₹1,200 is ₹1,200 × 15/100 = ₹180. Therefore, the sale price is ₹1,200 – ₹180 = ₹1,020.

 

Question 18:

Topic: Data Interpretation

Question: A pie chart shows that 50% of a company’s expenses are for salaries. If the total expenses are ₹800,000, how much is spent on salaries?

Options:

A. ₹350,000

B. ₹400,000

C. ₹450,000

D. ₹500,000

Correct Answer: B. ₹400,000

Explanation:

50% of the total expenses of ₹800,000 is allocated to salaries. This amount is ₹800,000 × 50/100 = ₹400,000.

 

Question 19:

Topic: Time and Speed

Question: A bus travels 180 km in 3 hours. What is its average speed in km/h?

Options:

A. 55 km/h

B. 60 km/h

C. 65 km/h

D. 70 km/h

Correct Answer: B. 60 km/h

Explanation:

The average speed of the bus is calculated by dividing the distance by the time. Therefore, the average speed is 180 km / 3 hours = 60 km/h.

 

Question 20:

Topic: Probability

Question: A box contains 7 red, 5 green, and 3 blue balls. What is the probability of drawing a green ball?

Options:

A. 1/4

B. 5/15

C. 1/3

D. 2/5

Correct Answer: C. 1/3

Explanation:

There are 5 green balls out of a total of 15 (7 red + 5 green + 3 blue). Therefore, the probability of drawing a green ball is 5/15 = 1/3.

 

Question 21:

Topic: Pipes and Cisterns

Question: Two pipes can fill a tank in 10 minutes and 20 minutes respectively. How long will it take to fill the tank if both pipes are opened together?

Options:

A. 6 minutes

B. 7 minutes

C. 8 minutes

D. 9 minutes

Correct Answer: B. 7 minutes

Explanation:

Pipe A fills 1/10 of the tank per minute, and pipe B fills 1/20 of the tank per minute. Together, they fill 1/10 + 1/20 = 3/20 of the tank per minute. Therefore, it will take approximately 7 minutes to fill the tank.

 

Question 22:

Topic: Profit and Loss

Question: A retailer buys a gadget for ₹600 and sells it for ₹750. What is the profit percentage?

Options:

A. 20%

B. 25%

C. 30%

D. 35%

Correct Answer: B. 25%

Explanation:

Profit = Selling Price – Cost Price = ₹750 – ₹600 = ₹150. Profit Percentage = (Profit / Cost Price) × 100 = (₹150/₹600) × 100 = 25%.

 

Question 23:

Topic: Number Series

Question: What is the next number in the series: 1, 4, 9, 16, …?

Options:

A. 20

B. 25

C. 30

D. 36

Correct Answer: B. 25

Explanation:

The series follows the pattern of squares: 1², 2², 3², 4², … The next number is 5² = 25.

 

Question 24:

Topic: Arithmetic Aptitude

Question: If 1/2 of a number is 8, what is the number?

Options:

A. 12

B. 14

C. 16

D. 18

Correct Answer: C. 16

Explanation:

Let the number be x. According to the problem, 1/2 of x is 8. So, x/2 = 8. Solving for x gives x = 16.

 

Question 25:

Topic: Mensuration

Question: What is the perimeter of a square with a side length of 6 cm?

Options:

A. 20 cm

B. 22 cm

C. 24 cm

D. 26 cm

Correct Answer: C. 24 cm

Explanation:

The perimeter of a square is 4 times the length of one side. Therefore, the perimeter is 4 × 6 cm = 24 cm.

 

Question 26:

Topic: Arithmetic Aptitude

Question: If 6 less than twice a number is 10, what is the number?

Options:

A. 6

B. 7

C. 8

D. 9

Correct Answer: C. 8

Explanation:

Let the number be x. According to the problem, 2x – 6 = 10. Solving for x gives x = 8.

 

Question 27:

Topic: Time and Speed

Question: If a train covers 300 km in 5 hours, what is its average speed in km/h?

Options:

A. 55 km/h

B. 60 km/h

C. 65 km/h

D. 70 km/h

Correct Answer: B. 60 km/h

Explanation:

The average speed of the train is calculated by dividing the distance by the time. Therefore, the average speed is 300 km / 5 hours = 60 km/h.

 

Question 28:

Topic: Probability

Question: A bag contains 4 red, 3 blue, and 2 green balls. What is the probability of drawing a red ball?

Options:

A. 2/9

B. 4/9

C. 1/3

D. 1/2

Correct Answer: B. 4/9

Explanation:

There are 4 red balls out of a total of 9 (4 red + 3 blue + 2 green). Therefore, the probability of drawing a red ball is 4/9.

 

Question 29:

Topic: Percentages

Question: If a person’s salary is increased by 25% to ₹50,000, what was their original salary?

Options:

A. ₹38,000

B. ₹40,000

C. ₹42,000

D. ₹45,000

Correct Answer: B. ₹40,000

Explanation:

Let the original salary be x. A 25% increase means the salary becomes x + 25% of x. So, x + 0.25x = ₹50,000. Solving for x gives x = ₹40,000.

 

Question 30:

Topic: Mensuration

Question: What is the volume of a cylinder with a radius of 3 cm and a height of 7 cm?

Options:

A. 63 cm³

B. 126 cm³

C. 189 cm³

D. 198 cm³

Correct Answer: C. 189 cm³

Explanation:

Volume of a cylinder = πr²h. So, volume = π × 3² × 7 = 22/7 × 9 × 7 ≈ 189 cm³.

 

Question 31:

Topic: Data Interpretation

Question: In a histogram, the sales of a product in the first quarter were 400 units, and in the second quarter, they were 520 units. What is the percentage increase?

Options:

A. 25%

B. 30%

C. 35%

D. 40%

Correct Answer: B. 30%

Explanation:

The increase is 520 – 400 = 120 units. The percentage increase is (120/400) × 100 = 30%.

 

Question 32:

Topic: Pipes and Cisterns

Question: If one tap can fill a tank in 25 minutes, and another can fill the same tank in 40 minutes, how long will it take for both taps to fill the tank together?

Options:

A. 12 minutes

B. 15 minutes

C. 17 minutes

D. 20 minutes

Correct Answer: B. 15 minutes

Explanation:

Tap A fills 1/25 of the tank per minute, and tap B fills 1/40. Together, they fill 1/25 + 1/40 = 13/200 of the tank per minute. Therefore, it will take 200/13 ≈ 15 minutes to fill the tank.

 

Question 33:

Topic: Profit and Loss

Question: A retailer buys a device for ₹700 and sells it for ₹850. What is the profit percentage?

Options:

A. 18%

B. 21%

C. 25%

D. 30%

Correct Answer: B. 21%

Explanation:

Profit = Selling Price – Cost Price = ₹850 – ₹700 = ₹150. Profit Percentage = (Profit / Cost Price) × 100 = (₹150/₹700) × 100 = 21%.

 

Question 34:

Topic: Number Series

Question: What is the next number in the series: 5, 10, 20, 40, …?

Options:

A. 60

B. 70

C. 80

D. 90

Correct Answer: C. 80

Explanation:

The series is doubling each term: 5, 5 × 2, 10 × 2, 20 × 2, … The next number is 40 × 2 = 80.

 

Question 35:

Topic: Arithmetic Aptitude

Question: If 3 times a number plus 10 equals 31, what is the number?

Options:

A. 5

B. 6

C. 7

D. 8

Correct Answer: C. 7

Explanation:

Let the number be x. According to the problem, 3x + 10 = 31. Solving for x gives x = 7.

 

Question 36:

Topic: Arithmetic Aptitude

Question: If 5 times a number plus 6 equals 56, what is the number?

Options:

A. 8

B. 9

C. 10

D. 11

Correct Answer: C. 10

Explanation:

Let the number be x. According to the problem, 5x + 6 = 56. Solving for x gives x = 10.

 

Question 37:

Topic: Time and Speed

Question: If a scooter travels 90 kilometers in 1.5 hours, what is its average speed in km/h?

Options:

A. 50 km/h

B. 55 km/h

C. 60 km/h

D. 65 km/h

Correct Answer: C. 60 km/h

Explanation:

The average speed of the scooter is calculated by dividing the distance by the time. Therefore, the average speed is 90 km / 1.5 hours = 60 km/h.

 

Question 38:

Topic: Probability

Question: A box contains 4 yellow, 3 green, and 5 red balls. What is the probability of drawing a yellow ball?

Options:

A. 1/4

B. 2/5

C. 4/12

D. 1/3

Correct Answer: C. 4/12

Explanation:

There are 4 yellow balls out of a total of 12 (4 yellow + 3 green + 5 red). Therefore, the probability of drawing a yellow ball is 4/12.

 

Question 39:

Topic: Percentages

Question: If a person’s salary increases from ₹40,000 to ₹48,000, what is the percentage increase?

Options:

A. 18%

B. 20%

C. 22%

D. 25%

Correct Answer: B. 20%

Explanation:

The increase in salary is ₹48,000 – ₹40,000 = ₹8,000. The percentage increase is (₹8,000/₹40,000) × 100 = 20%.

 

Question 40:

Topic: Mensuration

Question: What is the area of a triangle with a base of 10 cm and a height of 6 cm?

Options:

A. 25 cm²

B. 30 cm²

C. 35 cm²

D. 40 cm²

Correct Answer: B. 30 cm²

Explanation:

Area of a triangle = 1/2 × base × height. So, area = 1/2 × 10 cm × 6 cm = 30 cm².

 

Question 41:

Topic: Data Interpretation

Question: In a line chart, the sales of a company in 2017 were ₹300,000, and in 2018 it was ₹360,000. What is the percentage increase?

Options:

A. 15%

B. 18%

C. 20%

D. 25%

Correct Answer: C. 20%

Explanation:

The increase in sales is ₹360,000 – ₹300,000 = ₹60,000. The percentage increase is (₹60,000/₹300,000) × 100 = 20%.

 

Question 42:

Topic: Pipes and Cisterns

Question: If one tap can fill a tank in 15 minutes, and another can fill the same tank in 25 minutes, how long will it take for both taps to fill the tank together?

Options:

A. 8 minutes

B. 9 minutes

C. 10 minutes

D. 12 minutes

Correct Answer: B. 9 minutes

Explanation:

Tap A fills 1/15 of the tank per minute, and tap B fills 1/25. Together, they fill 1/15 + 1/25 = 8/75 of the tank per minute. Therefore, it will take 75/8 ≈ 9 minutes to fill the tank.

 

Question 43:

Topic: Profit and Loss

Question: A merchant buys a watch for ₹600 and sells it for ₹750. What is the profit percentage?

Options:

A. 20%

B. 25%

C. 30%

D. 35%

Correct Answer: B. 25%

Explanation:

Profit = Selling Price – Cost Price = ₹750 – ₹600 = ₹150. Profit Percentage = (Profit / Cost Price) × 100 = (₹150/₹600) × 100 = 25%.

 

Question 44:

Topic: Number Series

Question: What is the next number in the series: 2, 4, 8, 16, …?

Options:

A. 24

B. 28

C. 32

D. 36

Correct Answer: C. 32

Explanation:

The series is doubling each term: 2, 2 × 2, 4 × 2, 8 × 2, … The next number is 16 × 2 = 32.

 

Question 45:

Topic: Arithmetic Aptitude

Question: If 7 times a number minus 2 equals 26, what is the number?

Options:

A. 3

B. 4

C. 5

D. 6

Correct Answer: B. 4

Explanation:

Let the number be x. According to the problem, 7x – 2 = 26. Solving for x gives x = 4.

 

Question 46:

Topic: Arithmetic Aptitude

Question: If 9 subtracted from four times a number is 23, what is the number?

Options:

A. 6

B. 7

C. 8

D. 9

Correct Answer: C. 8

Explanation:

Let the number be x. According to the problem, 4x – 9 = 23. Solving for x gives x = 8.

 

Question 47:

Topic: Time and Speed

Question: If a motorcycle travels 160 kilometers in 2 hours, what is its average speed in km/h?

Options:

A. 70 km/h

B. 75 km/h

C. 80 km/h

D. 85 km/h

Correct Answer: C. 80 km/h

Explanation:

The average speed of the motorcycle is calculated by dividing the distance by the time. Therefore, the average speed is 160 km / 2 hours = 80 km/h.

 

Question 48:

Topic: Probability

Question: In a bag containing 6 red, 4 blue, and 2 green balls, what is the probability of drawing a blue ball?

Options:

A. 1/6

B. 1/4

C. 1/3

D. 2/5

Correct Answer: C. 1/3

Explanation:

There are 4 blue balls out of a total of 12 (6 red + 4 blue + 2 green). Therefore, the probability of drawing a blue ball is 4/12, which simplifies to 1/3.

 

Question 49:

Topic: Percentages

Question: If a jacket’s original price is ₹2,500 and it is sold at a 20% discount, what is the sale price?

Options:

A. ₹1,800

B. ₹2,000

C. ₹2,200

D. ₹2,300

Correct Answer: B. ₹2,000

Explanation:

A 20% discount on ₹2,500 is ₹2,500 × 20/100 = ₹500. Therefore, the sale price is ₹2,500 – ₹500 = ₹2,000.

 

Question 50:

Topic: Mensuration

Question: What is the perimeter of a rectangle with a length of 8 cm and a width of 6 cm?

Options:

A. 26 cm

B. 28 cm

C. 30 cm

D. 32 cm

Correct Answer: B. 28 cm

Explanation:

The perimeter of a rectangle is 2 × (length + width). Therefore, the perimeter is 2 × (8 cm + 6 cm) = 28 cm.

 

Question 51:

Topic: Data Interpretation

Question: In a bar chart, if the revenue of a company in one year is ₹500,000 and in the next year it is ₹600,000, what is the percentage increase?

Options:

A. 18%

B. 20%

C. 22%

D. 25%

Correct Answer: B. 20%

Explanation:

The increase in revenue is ₹600,000 – ₹500,000 = ₹100,000. The percentage increase is (₹100,000/₹500,000) × 100 = 20%.

 

Question 52:

Topic: Pipes and Cisterns

Question: If two pipes can fill a tank in 12 minutes and 18 minutes respectively, how long will it take to fill the tank if both pipes are opened together?

Options:

A. 6 minutes

B. 7 minutes

C. 8 minutes

D. 9 minutes

Correct Answer: B. 7 minutes

Explanation:

Pipe A fills 1/12 of the tank per minute, and pipe B fills 1/18 of the tank per minute. Together, they fill 1/12 + 1/18 = 5/36 of the tank per minute. Therefore, it will take approximately 7 minutes to fill the tank.

 

Question 53:

Topic: Profit and Loss

Question: A shopkeeper buys an item for ₹400 and sells it for ₹520. What is the profit percentage?

Options:

A. 25%

B. 30%

C. 35%

D. 40%

Correct Answer: B. 30%

Explanation:

Profit = Selling Price – Cost Price = ₹520 – ₹400 = ₹120. Profit Percentage = (Profit / Cost Price) × 100 = (₹120/₹400) × 100 = 30%.

 

Question 54:

Topic: Number Series

Question: What is the next number in the series: 3, 6, 11, 18, …?

Options:

A. 25

B. 27

C. 29

D. 31

Correct Answer: B. 27

Explanation:

The pattern involves adding consecutive prime numbers: 3, 3+3, 6+5, 11+7, … The next number is 18 + 9 = 27.

 

Question 55:

Topic: Arithmetic Aptitude

Question: If 8 added to three times a number is 44, what is the number?

Options:

A. 10

B. 11

C. 12

D. 13

Correct Answer: C. 12

Explanation:

Let the number be x. According to the problem, 3x + 8 = 44. Solving for x gives x = 12.