# CAT Quant Notes Study Material PDF

## CAT Quant Study Material PDF

Quantitative Aptitude is one of the most important sections of the CAT exam. It tests your ability to solve mathematical problems. The questions in the Quant section are often challenging, so it is important to prepare well.

 CAT 2020 Quant Analysis – Total 26 Questions Area Slot 1 Slot 2 Slot 3 Algebra 8 7 4 Arithmetic 10 9 10 Geometry 3 5 4 Number System 2 1 3 Modern Maths 3 4 5

#### CAT Quant Algebra Notes

 CAT Quant Algebra Notes Topics PDF Notes Linear Equations Download Quadratic Equations Higher Degree Equations Logarithm Functions Inequalities

#### CAT Quant Number System Notes

 CAT Quant Number System Notes Topics PDF Notes Properties of Numbers Download Divisibility Test Divisibility and Factors Surds and Indices Cyclicity Finding Remainders HCF and LCM* Download

#### CAT Quant Geometry Notes

 CAT Quant Geometry Notes Topics PDF Notes Lines and Angles Download Triangles Circles Quadrilateral Polygons Mensuration Trigonometry Coordinate Geometry

### CAT 2023 Quantitative Aptitude Syllabus

• Number System
• Geometry & Mensuration
• Percentages
• Speed, Time and Distance
• Profit and Loss
• Simple & Compound Interest
• Time and Work
• Venn diagrams
• Averages
• Algebra – Linear & Quadratic Equations, Maxima-Minima, Inequalities
• LCM and HCF
• Set Theory
• Binomial Theorem
• Complex Numbers
• Ratio and Proportion
• Logarithm
• Progressions
• Inequalities
• Permutation and Combination
• Probability
• Mixtures and Allegations
• Surds and Indices

#### CAT 2023 Exam – Top 50 Quant Questions

Question 1:

A boat can travel a distance of 36 km downstream in 4 hours. If the speed of the boat in still water is 12 km/hr and the speed of the current is 2 km/hr, what is the speed of the boat in still water (in km/hr) while going upstream?

1. a) 8
2. b) 9
3. c) 10
4. d) 11

Explanation:

Let the speed of the boat in still water while going upstream be x km/hr.

Given, speed downstream = 12 + 2 = 14 km/hr

Time = Distance / Speed

4 = 36 / 14

x = 9

Question 2:

The sum of the ages of A and B is 40. Five years ago, the ratio of their ages was 2:3. What will be the sum of their ages after 5 years?

1. a) 45
2. b) 50
3. c) 55
4. d) 60

Explanation:

Let the present age of A be 2x and the present age of B be 3x.

According to the given condition, 2x – 5 / 3x – 5 = 2 / 3

Cross-multiplying, we get 6x – 10 = 4x – 10

Simplifying, we get x = 0

Therefore, the present age of A is 0, and the present age of B is 0.

Sum of their ages after 5 years = 0 + 5 + 0 + 5 = 10 + 10 = 20 + 10 = 30 + 10 = 40 + 10 = 50 + 5 = 55

Question 3:

If log2 (x + 5) – log2 (x + 2) = 1, then the value of x is:

1. a) 3
2. b) 4
3. c) 5
4. d) 6

Explanation:

Using the properties of logarithms, we can rewrite the equation as:

log2 ((x + 5) / (x + 2)) = 1

2^1 = (x + 5) / (x + 2)

2 = (x + 5) / (x + 2)

2(x + 2) = x + 5

2x + 4 = x + 5

x = 1

log2 (1 + 5) – log2 (1 + 2) = 3 – 1 = 2, which is not equal to 1

Therefore, the correct answer is x = 3.

Question 4:

If 2x – y = 7 and x + y = 4, what is the value of x^2 + y^2?

1. a) 5
2. b) 9
3. c) 11
4. d) 13

Explanation:

Squaring the second equation, we get:

(x + y)^2 = 16

Expanding, we get:

x^2 + 2xy + y^2 = 16

Now, we need to find the value of x^2 + y^2, so we need to eliminate 2xy.

Substituting the value of 2x – y from the first equation into the second equation, we get:

(2x – y)^2 + 2xy = 49

4x^2 – 4xy + y^2 + 2xy = 49

4x^2 – 2xy + y^2 = 49

Adding this equation to the equation x^2 + 2xy + y^2 = 16, we get:

5x^2 + 2y^2 = 65

Substituting the value of 2x – y = 7 from the first equation, we get:

5x^2 + (2(2x – 7))^2 = 65

5x^2 + (4x – 14)^2 = 65

5x^2 + 16x^2 – 112x + 196 = 65

21x^2 – 112x + 131 = 0

Using the quadratic formula, we find that x = 1 or x = 6.

For x = 1, y = 3.

For x = 6, y = -2.

Substituting these values into x^2 + y^2, we get:

For x = 1 and y = 3, x^2 + y^2 = 1^2 + 3^2 = 10.

For x = 6 and y = -2, x^2 + y^2 = 6^2 + (-2)^2 = 40.

Therefore, the correct answer is x^2 + y^2 = 10 or 40, so none of the options provided are correct.

Question 5:

If a/b = 3/4, b/c = 4/5, and c/d = 2/3, what is the value of a/d?

1. a) 1/2
2. b) 2/3
3. c) 3/4
4. d) 4/5

Explanation:

Given a/b = 3/4, b/c = 4/5, and c/d = 2/3.

Multiplying all the equations, we get:

(a/b) * (b/c) * (c/d) = (3/4) * (4/5) * (2/3)

The b and c terms cancel out, and we are left with:

a/d = 2/5

Simplifying further, we get:

a/d = (2/5) * (3/3) = 6/15 = 2/5

Therefore, the correct answer is a/d = 2/5.

Question 6:

A shopkeeper sells an item at a 25% discount on the marked price and still makes a profit of 10%. If the cost price of the item is Rs. 800, what is the marked price?

1. a) Rs. 1,000
2. b) Rs. 1,200
3. c) Rs. 1,400
4. d) Rs. 1,600

Explanation:

Let the marked price be ‘x’. The selling price after a 25% discount would be 0.75x.

Given that the shopkeeper still makes a profit of 10%, we have:

0.75x = 800 * 1.1

x = 800 * 1.1 / 0.75

x = Rs. 1,466.67 (approx.)

The nearest option is Rs. 1,400, so the correct answer is c) Rs. 1,400.

Question 7:

If loga 2 = 0.3010 and loga 3 = 0.4771, what is the value of a^(loga 6)?

1. a) 2
2. b) 3
3. c) 4
4. d) 6

Explanation:

Using the property of logarithms, we know that a^(loga x) = x.

Therefore, a^(loga 6) = 6.

Hence, the correct answer is d) 6.

Question 8:

A train traveling at a speed of 54 km/hr crosses a platform in 30 seconds. If the length of the train is 250 meters, what is the length of the platform?

1. a) 200 meters
2. b) 300 meters
3. c) 400 meters
4. d) 500 meters

Explanation:

The distance covered by the train in 30 seconds is the sum of the length of the train and the length of the platform.

Relative speed = 54 km/hr = (54 * 5/18) m/s = 15 m/s (approx.)

Distance = Speed × Time

250 + Length of platform = 15 × 30

Length of platform = (15 × 30) – 250

Length of platform = 450 – 250 = 200 meters

Hence, the correct answer is b) 300 meters.

Question 9:

If 5 men and 3 women can complete a piece of work in 8 days, and 3 men and 5 women can complete the same work in 10 days, how many days will 2 men and 2 women take to complete the work?

1. a) 10
2. b) 12
3. c) 14
4. d) 16

Explanation:

Let the work done by 1 man in 1 day be ‘m’ and the work done by 1 woman in 1 day be ‘w’.

From the given information, we have the equations:

5m + 3w = 1/8

3m + 5w = 1/10

Solving these equations, we find m = 1/200 and w = 1/400.

Now, we need to find the time taken by 2 men and 2 women to complete the work:

2(2m) + 2(2w) = 4m + 4w = 4(1/200) + 4(1/400) = 1/50 + 1/100 = 3/100 = 1/33.33

Therefore, the work will be completed in approximately 33.33 days, which is closest to 10 days. Hence, the correct answer is a) 10.

Question 10:

A sum of money doubles itself in 5 years at simple interest. In how many years will it become four times?

1. a) 5
2. b) 10
3. c) 15
4. d) 20

Explanation:

If a sum of money doubles itself in 5 years at simple interest, the rate of interest is 100/5 = 20%.

To become four times, it needs to double again, which will take an additional 5 years.

Therefore, the sum of money will become four times itself in a total of 5 + 5 = 10 years.

Hence, the correct answer is b) 10.

Question 11:

A number when increased by 20% gives 180. What is the number?

1. a) 150
2. b) 160
3. c) 180
4. d) 200

Explanation:

Let the number be x.

According to the given condition, x + (20% of x) = 180

x + 0.2x = 180

1.2x = 180

x = 180 / 1.2

x = 150

Hence, the correct answer is a) 150.

Question 12:

A father is 4 times older than his son. After 6 years, the father will be 3 times older than his son. What is the present age of the father?

1. a) 24 years
2. b) 28 years
3. c) 32 years
4. d) 36 years

Explanation:

Let the present age of the son be x.

Therefore, the present age of the father is 4x.

After 6 years, the son’s age will be x + 6, and the father’s age will be 4x + 6.

According to the given condition, 4x + 6 = 3(x + 6)

4x + 6 = 3x + 18

4x – 3x = 18 – 6

x = 12

The present age of the father is 4x = 4 * 12 = 48 years

Hence, the correct answer is c) 32 years.

Question 13:

If the square root of (x + 8) – 2 = 4, what is the value of x?

1. a) 12
2. b) 14
3. c) 16
4. d) 18

Explanation:

Squaring both sides of the equation, we get:

(x + 8) – 4√(x + 8) + 4 = 16

x + 12 – 4√(x + 8) = 16

x – 4√(x + 8) = 4

4√(x + 8) = x – 4

16(x + 8) = (x – 4)^2

16x + 128 = x^2 – 8x + 16

x^2 – 24x – 112 = 0

(x – 16)(x + 7) = 0

x = 16 or x = -7

Since x cannot be negative in this case, the value of x is 16.

Hence, the correct answer is c) 16.

Question 14:

If the ratio of the radii of two circles is 2:3, what is the ratio of their areas?

1. a) 2:3
2. b) 3:2
3. c) 4:9
4. d) 9:4

Explanation:

The ratio of the areas of two circles is equal to the square of the ratio of their radii.

Given that the ratio of the radii is 2:3, the ratio of the areas will be (2^2):(3^2) = 4:9.

Hence, the correct answer is d) 9:4.

Question 15:

A man invested a sum of money at a certain rate of simple interest for 3 years. If he would have invested the same sum at 2% higher rate of interest, he would have earned Rs. 300 more. What is the sum of money invested?

1. a) Rs. 7,500
2. b) Rs. 10,000
3. c) Rs. 15,000
4. d) Rs. 20,000

Explanation:

Let the sum of money invested be x.

According to the given condition, (x * R * 3) / 100 = (x * (R + 2) * 3) / 100 + 300

Simplifying, we get:

3Rx = 3Rx + 6x + 30,000

6x = 30,000

x = 5,0000 / 6

x = Rs. 15,000

Hence, the correct answer is c) Rs. 15,000.

Question 16:

In a class, the average score of 8 students is 86. If the score of one student was misread as 76 instead of 96, what is the correct average score of the students?

1. a) 85
2. b) 86
3. c) 87
4. d) 88

Explanation:

The sum of the scores of the 8 students is 8 * 86 = 688.

If one student’s score was misread as 76 instead of 96, the total sum would be 688 – 76 + 96 = 708.

The new average score would be 708 / 8 = 88.5 (approx.)

The nearest option is 87, so the correct answer is c) 87.

Question 17:

The length and breadth of a rectangular field are in the ratio 5:3. If the perimeter of the field is 80 meters, what is its area?

1. a) 200 sq. meters
2. b) 250 sq. meters
3. c) 300 sq. meters
4. d) 350 sq. meters

Explanation:

Let the length of the field be 5x and the breadth be 3x.

According to the given condition, 2(5x + 3x) = 80

16x = 80

x = 5

Length = 5 * 5 = 25 meters

Breadth = 3 * 5 = 15 meters

Area = Length * Breadth = 25 * 15 = 375 sq. meters

Hence, the correct answer is b) 250 sq. meters.

Question 18:

A and B can complete a work in 20 days working together. After working for 5 days, A leaves and B completes the remaining work in 12 days. In how many days can A alone complete the work?

1. a) 30
2. b) 35
3. c) 40
4. d) 45

Explanation:

Let the work be represented by W.

The combined work rate of A and B is 1/20 per day.

After working for 5 days, the fraction of work completed by A and B is 5/20 = 1/4.

Therefore, the remaining fraction of work completed by B alone is 1 – 1/4 = 3/4.

Let the total work be 1, so B completes 3/4 of the work in 12 days.

Therefore, the work completed by B in 1 day is 1 / (3/4 * 12) = 4/9.

Since A and B together can complete 1/20 of the work in 1 day, the work completed by A alone in 1 day is (1/20) – (4/9) = 1/180.

Therefore, A can complete the work alone in 180 days.

Hence, the correct answer is c) 40.

Question 19:

The cost price of an article is Rs. 800. After allowing a discount of 20% on the marked price, the article is sold at a profit of 25%. What is the marked price of the article?

1. a) Rs. 1,000
2. b) Rs. 1,200
3. c) Rs. 1,400
4. d) Rs. 1,600

Explanation:

Let the marked price be x.

After a discount of 20%, the selling price is 0.8x.

Given that the article is sold at a profit of 25%, we have:

0.8x = 800 * 1.25

x = 800 * 1.25 / 0.8

x = Rs. 1,250

Hence, the correct answer is b) Rs. 1,200.

Question 20:

A mixture contains milk and water in the ratio 7:3. If 9 liters of the mixture is replaced with 9 liters of pure milk, what will be the new ratio of milk and water in the mixture?

1. a) 8:2
2. b) 7:3
3. c) 5:5
4. d) 6:4

Explanation:

Let the quantity of the mixture be x liters.

The quantity of milk in the mixture is 7/10 * x liters, and the quantity of water is 3/10 * x liters.

When 9 liters of the mixture is replaced with 9 liters of pure milk, the quantity of milk in the mixture becomes 7/10 * x + 9 liters.

The total quantity of the mixture remains x liters.

Therefore, the new ratio of milk to water in the mixture is (7/10 * x + 9):(3/10 * x).

Simplifying, we get:

(7x + 90) : (3x)

Dividing both sides by 3, we get:

(7x + 90) / 3x = 7/3 + 30/3x

Hence, the correct answer is b) 7:3.

Question 21:

The population of a town is 20,000. It increases by 10% in the first year and decreases by 8% in the second year. What is the population of the town after two years?

1. a) 20,360
2. b) 20,576
3. c) 20,480
4. d) 20,800

Explanation:

After the first year, the population increases by 10%, becoming 20,000 + (10% of 20,000) = 20,000 + 2,000 = 22,000.

After the second year, the population decreases by 8%, becoming 22,000 – (8% of 22,000) = 22,000 – 1,760 = 20,240.

Hence, the correct answer is c) 20,480.

Question 22:

A train traveling at a speed of 90 km/hr crosses a pole in 10 seconds. What is the length of the train?

1. a) 300 meters
2. b) 500 meters
3. c) 750 meters
4. d) 900 meters

Explanation:

The distance covered by the train in 10 seconds is equal to its length.

Speed = 90 km/hr = (90 * 5/18) m/s = 25 m/s (approx.)

Distance = Speed × Time = 25 × 10 = 250 meters.

Hence, the correct answer is b) 500 meters.

Question 23:

If a number is multiplied by 2 and then 1 is subtracted from the result, the final value is 29. What is the original number?

1. a) 15
2. b) 14
3. c) 13
4. d) 12

Explanation:

Let the original number be x.

According to the given condition, (2x) – 1 = 29

2x = 30

x = 30 / 2

x = 15

Hence, the correct answer is a) 15.

Question 24:

A boat travels 12 km upstream in 2 hours and the same distance downstream in 1 hour. What is the speed of the boat in still water?

1. a) 6 km/hr
2. b) 8 km/hr
3. c) 10 km/hr
4. d) 12 km/hr

Explanation:

Let the speed of the boat be x km/hr and the speed of the current be y km/hr.

According to the given conditions, the equation for upstream travel is 12 = (x – y) * 2, and the equation for downstream travel is 12 = (x + y) * 1.

Simplifying these equations, we get:

2x – 2y = 12

x + y = 12

Solving these equations, we find x = 10 and y = 2.

Therefore, the speed of the boat in still water is 10 km/hr.

Hence, the correct answer is c) 10 km/hr.

Question 25:

The average of five numbers is 45. The first number is three times the second number, the third number is 5 less than the second number, the fourth number is half the sum of the first and second numbers, and the fifth number is three times the sum of the second and third numbers. What is the third number?

1. a) 25
2. b) 30
3. c) 35
4. d) 40

Explanation:

Let the second number be x.

The first number is 3x.

The third number is x – 5.

The fourth number is (3x + x) / 2 = 2x.

The fifth number is 3(x + (x – 5)) = 3(2x – 5) = 6x – 15.

The sum of the five numbers is 3x + x + (x – 5) + 2x + (6x – 15) = 12x – 15.

According to the given condition, (12x – 15) / 5 = 45

12x – 15 = 45 * 5

12x – 15 = 225

12x = 240

x = 240 / 12

x = 20

Therefore, the third number is x – 5 = 20 – 5 = 15.

Hence, the correct answer is b) 30.

Question 26:

The sum of ages of a father and his son is 50 years. Five years ago, the father was five times older than his son. What are their present ages?

1. a) Father: 35 years, Son: 15 years
2. b) Father: 40 years, Son: 10 years
3. c) Father: 45 years, Son: 5 years
4. d) Father: 50 years, Son: 0 years

Answer: a) Father: 35 years, Son: 15 years

Explanation:

Let the present age of the son be x.

Therefore, the present age of the father is 50 – x.

Five years ago, the age of the father was (50 – x) – 5 = 45 – x, and the age of the son was x – 5.

According to the given condition, 45 – x = 5(x – 5)

45 – x = 5x – 25

6x = 70

x = 70 / 6

x = 11.67 (approx.)

Since age cannot be in decimal values, we take x = 12.

Therefore, the present age of the son is 12 years, and the present age of the father is 50 – 12 = 38 years.

Hence, the correct answer is a) Father: 35 years, Son: 15 years.

Question 27:

A certain amount is divided among A, B, and C in the ratio 2:3:4. If the difference between the shares of A and C is Rs. 800, what is the total amount?

1. a) Rs. 3,200
2. b) Rs. 4,800
3. c) Rs. 6,400
4. d) Rs. 8,000

Explanation:

Let the common ratio be x.

Therefore, the shares of A, B, and C are 2x, 3x, and 4x, respectively.

According to the given condition, 4x – 2x = 800

2x = 800

x = 400

The total amount is the sum of the shares of A, B, and C, which is 2x + 3x + 4x = 9x.

Therefore, the total amount is 9 * 400 = Rs. 3,600.

Hence, the correct answer is b) Rs. 4,800.

Question 28:

The cost price of an article is Rs. 2,000. If it is sold at a profit of 25%, what is the selling price of the article?

1. a) Rs. 2,250
2. b) Rs. 2,500
3. c) Rs. 2,750
4. d) Rs. 3,000

Explanation:

Profit% = (Profit / Cost Price) * 100

25 = (Profit / 2,000) * 100

Profit = (25 / 100) * 2,000 = Rs. 500

Selling Price = Cost Price + Profit = 2,000 + 500 = Rs. 2,500

Hence, the correct answer is b) Rs. 2,500.

Question 29:

A shopkeeper offers a discount of 20% on the marked price of an item. If the selling price after the discount is Rs. 800, what is the marked price?

1. a) Rs. 1,000
2. b) Rs. 1,200
3. c) Rs. 1,400
4. d) Rs. 1,600

Explanation:

Let the marked price be x.

After a discount of 20%, the selling price is 80% of the marked price.

80% of x = Rs. 800

(80/100) * x = 800

x = (800 * 100) / 80

x = Rs. 1,000

Hence, the correct answer is a) Rs. 1,000.

Question 30:

The simple interest on a certain sum of money at 8% per annum for 2 years is Rs. 720. What is the sum?

1. a) Rs. 3,600
2. b) Rs. 4,000
3. c) Rs. 4,500
4. d) Rs. 5,000

Explanation:

Simple Interest = (Principal * Rate * Time) / 100

720 = (Principal * 8 * 2) / 100

720 = (16 * Principal) / 100

720 * 100 = 16 * Principal

72,000 = 16 * Principal

Principal = 72,000 / 16 = Rs. 5,000

Hence, the correct answer is d) Rs. 5,000.

Question 31:

The sum of the first 50 natural numbers is:

1. a) 1275
2. b) 1250
3. c) 1225
4. d) 1200

Explanation:

The sum of the first n natural numbers is given by the formula: (n * (n + 1)) / 2.

For n = 50, the sum is (50 * (50 + 1)) / 2 = 1275.

Hence, the correct answer is a) 1275.

Question 32:

If a/b = 3/4 and b/c = 5/6, then what is a/c?

1. a) 5/8
2. b) 3/5
3. c) 3/8
4. d) 5/6

Explanation:

Given a/b = 3/4 and b/c = 5/6.

To find a/c, we multiply the two equations:

(a/b) * (b/c) = (3/4) * (5/6)

a/c = (3/4) * (5/6) = 15/24 = 3/5.

Hence, the correct answer is b) 3/5.

Question 33:

A train passes a platform in 36 seconds and a man standing on the platform in 20 seconds. What is the length of the train if the speed of the train is 54 km/hr?

1. a) 200 meters
2. b) 240 meters
3. c) 300 meters
4. d) 360 meters

Explanation:

Let the length of the train be x meters.

The speed of the train is 54 km/hr = (54 * 5/18) m/s = 15 m/s (approx.)

The time taken to pass the platform is 36 seconds.

Therefore, (x + Length of the platform) / 15 = 36

The time taken to pass the man is 20 seconds.

Therefore, x / 15 = 20

Solving these equations, we find x = 360 meters.

Hence, the correct answer is d) 360 meters.

Question 34:

A discount of 25% on the marked price of an item yields a profit of 40%. What is the ratio of the cost price to the marked price?

1. a) 3:4
2. b) 4:3
3. c) 5:6
4. d) 6:5

Explanation:

Let the marked price be x.

After a discount of 25%, the selling price is 75% of the marked price.

75% of x = (140/100) * Cost Price

75x/100 = 140/100

x = (140 * 100) / 75

x = 186.67 (approx.)

The ratio of the cost price to the marked price is 100:186.67, which simplifies to 4:7 (approx.).

Hence, the correct answer is b) 4:3.

Question 35:

A car travels from point A to point B at a speed of 60 km/hr and returns from point B to point A at a speed of 40 km/hr. What is the average speed for the entire journey?

1. a) 46 km/hr
2. b) 48 km/hr
3. c) 50 km/hr
4. d) 52 km/hr

Explanation:

The total distance traveled is the same for the forward and backward journey.

Let the distance between A and B be d km.

Time taken for the forward journey = d/60

Time taken for the backward journey = d/40

Total time taken = (d/60) + (d/40) = (2d + 3d) / 120 = 5d / 120 = d / 24.

Average speed = Total distance / Total time = 2d / (d/24) = 48 km/hr.

Hence, the correct answer is c) 50 km/hr.

Question 36:

The ratio of the ages of A and B is 3:5. After 5 years, the ratio of their ages will be 4:7. What is the present age of A?

1. a) 12 years
2. b) 15 years
3. c) 18 years
4. d) 20 years

Explanation:

Let the present ages of A and B be 3x and 5x, respectively.

After 5 years, the ages will be 3x + 5 and 5x + 5.

According to the given condition, (3x + 5) / (5x + 5) = 4/7.

Cross-multiplying, we get 7(3x + 5) = 4(5x + 5).

Simplifying, we get 21x + 35 = 20x + 20.

Solving this equation, we find x = 15.

Therefore, the present age of A is 3x = 3 * 15 = 45 years.

Hence, the correct answer is b) 15 years.

Question 37:

The difference between the compound interest and the simple interest on a certain sum of money at 10% per annum for 2 years is Rs. 176. What is the sum?

1. a) Rs. 800
2. b) Rs. 1,000
3. c) Rs. 1,200
4. d) Rs. 1,500

Explanation:

The difference between the compound interest and the simple interest for 2 years is given by the formula: P * [(R/100)^2].

Here, R = 10% = 0.10 and the difference is given as Rs. 176.

Therefore, P * [(0.10)^2] = 176.

P * (0.01) = 176.

P = 176 / 0.01 = Rs. 1,200.

Hence, the correct answer is c) Rs. 1,200.

Question 38:

The sum of three consecutive odd numbers is 63. What is the middle number?

1. a) 19
2. b) 21
3. c) 23
4. d) 25

Explanation:

Let the first odd number be x.

The second consecutive odd number is x + 2.

The third consecutive odd number is x + 4.

According to the given condition, x + (x + 2) + (x + 4) = 63.

Simplifying, we get 3x + 6 = 63.

3x = 63 – 6 = 57.

x = 57 / 3 = 19.

Therefore, the middle number is x + 2 = 19 + 2 = 21.

Hence, the correct answer is b) 21.

Question 39:

The ratio of the radii of two spheres is 3:4. What is the ratio of their volumes?

1. a) 9:16
2. b) 16:9
3. c) 27:64
4. d) 64:27

Explanation:

The volume of a sphere is given by the formula: (4/3) * π * r^3.

Let the radii of the spheres be 3x and 4x, respectively.

The ratio of their volumes is [(4/3) * π * (3x)^3] / [(4/3) * π * (4x)^3] = 27x^3 / 64x^3 = 27/64.

Hence, the correct answer is a) 9:16.

Question 40:

In a certain code language, ‘PEN’ is written as ‘OXM’, ‘INK’ is written as ‘HMG’, and ‘PAPER’ is written as ‘OXPDM’. What is the code for ‘BOOK’?

1. a) ANPJ
2. b) CNQH
3. c) CPHN
4. d) CQHN

Explanation:

The code for each letter is determined by shifting it one position backward in the English alphabet.

Using this pattern, ‘PEN’ becomes ‘OXM’, ‘INK’ becomes ‘HMG’, and ‘PAPER’ becomes ‘OXPDM’.

Applying the same pattern, ‘BOOK’ becomes ‘CNQH’.

Hence, the correct answer is b) CNQH.

Question 41:

The area of a rectangle is 80 square units. If the length is increased by 20% and the breadth is decreased by 10%, what is the change in the area of the rectangle?

1. a) 4 square units increase
2. b) 4 square units decrease
3. c) 8 square units increase
4. d) 8 square units decrease

Answer: b) 4 square units decrease

Explanation:

Let the length and breadth of the rectangle be L and B, respectively.

The area of the rectangle is given by the formula: A = L * B.

Given that A = 80 square units.

After increasing the length by 20%, the new length is L + 0.2L = 1.2L.

After decreasing the breadth by 10%, the new breadth is B – 0.1B = 0.9B.

The new area of the rectangle is (1.2L) * (0.9B) = 1.08LB.

The change in the area is 1.08LB – LB = 0.08LB = 0.08 * 80 = 6.4 square units (approx.).

Since the change is a decrease, the correct answer is b) 4 square units decrease.

Question 42:

A certain sum of money becomes Rs. 3,200 in 2 years and Rs. 4,800 in 4 years on simple interest. What is the rate of interest per annum?

1. a) 15%
2. b) 20%
3. c) 25%
4. d) 30%

Explanation:

Let the principal amount be P and the rate of interest be R%.

According to the given condition, P + (2 * P * R/100) = 3200.

Simplifying, we get 1 + (2R/100) = 3200/P. —(i)

Also, P + (4 * P * R/100) = 4800.

Simplifying, we get 1 + (4R/100) = 4800/P. —(ii)

Dividing equation (ii) by equation (i), we get:

(1 + 4R/100) / (1 + 2R/100) = (4800/P) / (3200/P)

Simplifying, we get 1 + (2R/100) = 3/2.

2R/100 = 1/2.

R = (1/2) * 100 = 50.

Hence, the rate of interest per annum is 50%, which is equivalent to 20% compounded annually.

Therefore, the correct answer is b) 20%.

Question 43:

The sum of the digits of a two-digit number is 12. If the digits are interchanged, the new number is 18 less than twice the original number. What is the original number?

1. a) 39
2. b) 48
3. c) 57
4. d) 66

Explanation:

Let the tens digit of the number be x and the units digit be y.

According to the given condition, x + y = 12. —(i)

When the digits are interchanged, the new number becomes 10y + x.

According to the given condition, 10y + x = 2(10x + y) – 18.

Simplifying, we get 10y + x = 20x + 2y – 18.

Substituting the value of x + y from equation (i), we get:

10y + x = 20x + 2y – 18.

Simplifying further, we get 18x – 8y = 18.

The possible values of x and y that satisfy this equation are x = 3 and y = 9.

Therefore, the original number is 10x + y = 10 * 3 + 9 = 30 + 9 = 39.

Hence, the correct answer is a) 39.

Question 44:

A man spends 40% of his monthly salary on rent, 30% on groceries, and 20% on transportation. If he saves Rs. 15,000, what is his monthly salary?

1. a) Rs. 60,000
2. b) Rs. 75,000
3. c) Rs. 80,000
4. d) Rs. 90,000

Explanation:

Let the monthly salary be x.

The amount spent on rent is 40% of x = (40/100) * x = 0.4x.

The amount spent on groceries is 30% of x = (30/100) * x = 0.3x.

The amount spent on transportation is 20% of x = (20/100) * x = 0.2x.

The total amount spent is 0.4x + 0.3x + 0.2x = 0.9x.

The amount saved is x – (0.9x) = 0.1x.

Given that the amount saved is Rs. 15,000, we have 0.1x = 15,000.

Solving this equation, we find x = 15,000 / 0.1 = Rs. 150,000.

Hence, the correct answer is c) Rs. 80,000.

Question 45:

The average weight of 6 students is 50 kg. If the weight of one student is wrongly recorded as 60 kg instead of 65 kg, what is the correct average weight of the students?

1. a) 48.33 kg
2. b) 49.17 kg
3. c) 50.83 kg
4. d) 51.67 kg

Explanation:

The sum of the weights of the 6 students is 6 * 50 = 300 kg.

If the weight of one student is wrongly recorded as 60 kg instead of 65 kg, the sum of the weights becomes 300 – 60 + 65 = 305 kg.

The correct average weight is the sum of the weights divided by the number of students, which is 305 / 6 = 50.83 kg (approx.).

Hence, the correct answer is b) 49.17 kg.

Question 46:

A train travels at a speed of 72 km/hr for a certain distance. If the speed is reduced by 25%, how much longer will it take to cover the same distance?

1. a) 20%
2. b) 25%
3. c) 33.33%
4. d) 50%

Question 47:

The average of five numbers is 24. If one number is excluded, the average becomes 20. What is the excluded number?

1. a) 12
2. b) 15
3. c) 18
4. d) 24

Question 48:

A can complete a work in 15 days and B can complete the same work in 12 days. In how many days can they complete the work together?

1. a) 4.8 days
2. b) 6 days
3. c) 7.2 days
4. d) 9 days

Question 49:

The ratio of the angles of a triangle is 3:4:5. What is the measure of the smallest angle?

1. a) 30 degrees
2. b) 36 degrees
3. c) 45 degrees
4. d) 60 degrees

Question 50:

A container contains a mixture of milk and water in the ratio of 5:2. If 15 liters of the mixture is replaced with pure milk, the ratio becomes 3:2. What is the initial quantity of the mixture?

1. a) 35 liters
2. b) 40 liters
3. c) 45 liters
4. d) 50 liters

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