Assam Government Grade 4 | ( Mathematics ) Must Know Question Answers

Question 31:
Topic: Percentages
Question: If a person spends 30% of his salary on rent and the rent is ₹6,000, what is his total salary?
Options:
A. ₹18,000
B. ₹20,000
C. ₹22,000
D. ₹25,000
Correct Answer: B. ₹20,000
Explanation:
30% of his salary is ₹6,000. Therefore, his total salary is ₹6,000 / 30% = ₹6,000 / 0.30 = ₹20,000.

Question 32:
Topic: Arithmetic Aptitude
Question: If 40% of a number is 80, what is 60% of that number?
Options:
A. 100
B. 120
C. 140
D. 160
Correct Answer: B. 120
Explanation:
40% of the number is 80, so the number is 80 / 40% = 80 / 0.40 = 200. Therefore, 60% of this number is 200 × 60% = 200 × 0.60 = 120.

Question 33:
Topic: Data Interpretation
Question: A pie chart shows that 60% of a company’s employees are male. If the total number of employees is 500, how many are female?
Options:
A. 200
B. 250
C. 300
D. 350
Correct Answer: A. 200
Explanation:
60% of the employees are male, so 40% are female. Therefore, the number of female employees is 500 × 40% = 500 × 0.40 = 200.

Question 34:
Topic: Time and Speed
Question: A bus travels 150 km in 2.5 hours. What is the average speed of the bus 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 bus is calculated by dividing the distance by the time. Therefore, the average speed is 150 km / 2.5 hours = 60 km/h.

Question 35:
Topic: Probability
Question: A box contains 4 blue, 3 red, and 2 green marbles. What is the probability of drawing a red marble?
Options:
A. 1/3
B. 1/4
C. 1/5
D. 1/9
Correct Answer: A. 1/3
Explanation:
There are 3 red marbles out of a total of 9 (4 blue + 3 red + 2 green). Therefore, the probability of drawing a red marble is 3/9 = 1/3.

Question 36:
Topic: Pipes and Cisterns
Question: Pipe A can fill a tank in 40 minutes, and pipe B can empty it in 60 minutes. If both pipes are opened together, how long will it take to fill the tank?
Options:
A. 120 minutes
B. 100 minutes
C. 80 minutes
D. 60 minutes
Correct Answer: A. 120 minutes
Explanation:
Pipe A fills 1/40 of the tank per minute, and pipe B empties 1/60 of the tank per minute. Together, they fill 1/40 – 1/60 = 1/120 of the tank per minute. Therefore, it will take 120 minutes to fill the tank.

Question 37:
Topic: Percentages
Question: A student scores 45 out of 60 in a test. What percentage did the student score?
Options:
A. 70%
B. 75%
C. 80%
D. 85%
Correct Answer: B. 75%
Explanation:
The percentage score is calculated by dividing the obtained marks by the total marks and then multiplying by 100. Therefore, the percentage score is (45 / 60) × 100 = 75%.

Question 38:
Topic: Arithmetic Aptitude
Question: What is 30% of 150?
Options:
A. 35
B. 40
C. 45
D. 50
Correct Answer: C. 45
Explanation:
30% of 150 is calculated as 150 × 30/100 = 45.

Question 39:
Topic: Data Interpretation
Question: A bar graph shows the number of cars sold by a dealership each month. If 40 cars were sold in January, 50 in February, and 30 in March, what is the average number of cars sold per month?
Options:
A. 35
B. 40
C. 45
D. 50
Correct Answer: B. 40
Explanation:
The average number of cars sold per month is calculated by dividing the total number of cars sold by the number of months. So, the average is (40 + 50 + 30) / 3 = 120 / 3 = 40.

Question 40:
Topic: Time and Speed
Question: A cyclist covers a distance of 80 km in 4 hours. What is her average speed in km/h?
Options:
A. 18 km/h
B. 20 km/h
C. 22 km/h
D. 25 km/h
Correct Answer: B. 20 km/h
Explanation:
The average speed of the cyclist is calculated by dividing the distance by the time. Therefore, the average speed is 80 km / 4 hours = 20 km/h.

Question 41:
Topic: Profit and Loss
Question: A trader buys goods for ₹1,200 and sells them for ₹1,500. What is his profit percentage?
Options:
A. 20%
B. 25%
C. 30%
D. 35%
Correct Answer: B. 25%
Explanation:
The profit is the selling price minus the cost price, which is ₹1,500 – ₹1,200 = ₹300. The profit percentage is (₹300/₹1,200) × 100 = 25%.

Question 42:
Topic: Mensuration
Question: What is the area of a triangle with a base of 10 cm and a height of 8 cm?
Options:
A. 35 cm²
B. 40 cm²
C. 45 cm²
D. 50 cm²
Correct Answer: B. 40 cm²
Explanation:
The area of a triangle is calculated as 1/2 × base × height. Therefore, the area is 1/2 × 10 cm × 8 cm = 40 cm².

Question 43:
Topic: Arithmetic Aptitude
Question: If the sum of three consecutive even numbers is 54, what is the smallest number?
Options:
A. 16
B. 18
C. 20
D. 22
Correct Answer: A. 16
Explanation:
Let the three consecutive even numbers be x, x + 2, and x + 4. Their sum is x + (x + 2) + (x + 4) = 54. Solving for x gives x = 16.

Question 44:
Topic: Data Interpretation
Question: If a line graph indicates that a company’s profit increased from ₹200,000 in the first quarter to ₹250,000 in the second quarter, what is the percentage increase?
Options:
A. 20%
B. 25%
C. 30%
D. 35%
Correct Answer: B. 25%
Explanation:
The increase in profit is ₹250,000 – ₹200,000 = ₹50,000. The percentage increase is (₹50,000/₹200,000) × 100 = 25%.

Question 45:
Topic: Time and Speed
Question: A train travels 480 km in 8 hours. What is its 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 speed of the train is calculated by dividing the distance by the time. Therefore, the speed of the train is 480 km / 8 hours = 60 km/h.

Question 46:
Topic: Percentages
Question: If a product’s price is increased by 25% and then decreased by 20%, what is the final percentage change in the price?
Options:
A. 5% increase
B. 5% decrease
C. 10% increase
D. No change
Correct Answer: A. 5% increase
Explanation:
A 25% increase followed by a 20% decrease is calculated as an overall change of (1 + 25/100) × (1 – 20/100) = 1.25 × 0.80 = 1.00 = 100% of the original price, which is no change.

Question 47:
Topic: Arithmetic Aptitude
Question: What is 60% of 120?
Options:
A. 62
B. 68
C. 72
D. 76
Correct Answer: C. 72
Explanation:
60% of 120 is calculated as 120 × 60/100 = 72.

Question 48:
Topic: Data Interpretation
Question: In a pie chart, if the sector representing entertainment expenses is 72 degrees, what percentage of the total expenses is spent on entertainment?
Options:
A. 10%
B. 15%
C. 20%
D. 25%
Correct Answer: C. 20%
Explanation:
A full circle in a pie chart represents 100% and has 360 degrees. Therefore, each degree represents (100/360)% of the total. A 72-degree sector represents 72 × (100/360)% = 20% of the total expenses.

Question 49:
Topic: Time and Speed
Question: A car travels 180 km in 3 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 car is calculated by dividing the distance by the time. Therefore, the average speed is 180 km / 3 hours = 60 km/h.

Question 50:
Topic: Probability
Question: A bag contains 6 red and 4 blue balls. What is the probability of drawing a blue ball?
Options:
A. 2/5
B. 1/3
C. 1/2
D. 3/5
Correct Answer: A. 2/5
Explanation:
There are 4 blue balls out of a total of 10 (6 red + 4 blue). Therefore, the probability of drawing a blue ball is 4/10 = 2/5.

Question 51:
Topic: Pipes and Cisterns
Question: If one pipe can fill a tank in 30 minutes and another can empty it in 45 minutes, when both pipes are opened together, how long will it take to fill the tank?
Options:
A. 70 minutes
B. 90 minutes
C. 110 minutes
D. 130 minutes
Correct Answer: B. 90 minutes
Explanation:
The first pipe fills 1/30 of the tank per minute, and the second pipe empties 1/45 of the tank per minute. Together, they fill 1/30 – 1/45 = 1/90 of the tank per minute. Therefore, it will take 90 minutes to fill the tank.

Question 52:
Topic: Percentages
Question: If a person’s income is increased by 15% and then reduced by 10%, what is the final percentage change in his income?
Options:
A. 4.5% increase
B. 5% increase
C. 5.5% increase
D. 6% increase
Correct Answer: A. 4.5% increase

Question 61:
Topic: Percentages
Question: If a student scores 90 out of 120 in a test, what percentage did the student achieve?
Options:
A. 70%
B. 75%
C. 80%
D. 85%
Correct Answer: B. 75%
Explanation:
The percentage score is calculated by dividing the obtained marks by the total marks and then multiplying by 100. Therefore, the percentage score is (90 / 120) × 100 = 75%.

Question 62:
Topic: Arithmetic Aptitude
Question: What is 45% of 200?
Options:
A. 80
B. 90
C. 100
D. 110
Correct Answer: B. 90
Explanation:
45% of 200 is calculated as 200 × 45/100 = 90.

Question 63:
Topic: Data Interpretation
Question: A line graph shows that a company’s revenue decreased from ₹500,000 in one quarter to ₹450,000 in the next. What is the percentage decrease?
Options:
A. 8%
B. 10%
C. 12%
D. 15%
Correct Answer: B. 10%
Explanation:
The decrease in revenue is ₹500,000 – ₹450,000 = ₹50,000. The percentage decrease is (₹50,000/₹500,000) × 100 = 10%.

Question 64:
Topic: Time and Speed
Question: A vehicle travels 240 km in 4 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 vehicle is calculated by dividing the distance by the time. Therefore, the average speed is 240 km / 4 hours = 60 km/h.

Question 65:
Topic: Probability
Question: A bag contains 5 green, 4 yellow, and 3 blue balls. What is the probability of drawing a yellow ball?
Options:
A. 1/4
B. 1/3
C. 2/5
D. 3/5
Correct Answer: B. 1/3
Explanation:
There are 4 yellow balls out of a total of 12 (5 green + 4 yellow + 3 blue). Therefore, the probability of drawing a yellow ball is 4/12 = 1/3.

Question 66:
Topic: Pipes and Cisterns
Question: Two pipes can fill a tank in 20 and 30 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?
Options:
A. 12 minutes
B. 15 minutes
C. 18 minutes
D. 20 minutes
Correct Answer: A. 12 minutes
Explanation:
The first pipe fills 1/20 of the tank per minute, and the second pipe fills 1/30 of the tank per minute. Together, they fill 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12 of the tank per minute. Therefore, the tank will be filled in 12 minutes.

Question 67:
Topic: Percentages
Question: A shopkeeper marks up the price of an item by 40% and then offers a discount of 15%. What is the overall percentage change in the price?
Options:
A. 19% increase
B. 21% increase
C. 23% increase
D. 25% increase
Correct Answer: A. 19% increase
Explanation:
A 40% markup followed by a 15% discount is calculated as an overall increase of (1 + 40/100) × (1 – 15/100) = 1.40 × 0.85 = 1.19 = 119% of the original price, which is a 19% increase.

Question 68:
Topic: Arithmetic Aptitude
Question: What is 20% of 250?
Options:
A. 45
B. 50
C. 55
D. 60
Correct Answer: B. 50
Explanation:
20% of 250 is calculated as 250 × 20/100 = 50.

Question 69:
Topic: Data Interpretation
Question: If a bar graph indicates that a store sold 200 items in April and 180 items in May, what is the percentage decrease in sales?
Options:
A. 8%
B. 10%
C. 12%
D. 15%
Correct Answer: B. 10%
Explanation:
The decrease in sales is 200 – 180 = 20 items. The percentage decrease is (20/200) × 100 = 10%.

Question 70:
Topic: Time and Speed
Question: A runner completes a 300-meter race in 30 seconds. What is the average speed of the runner in meters per second?
Options:
A. 8 m/s
B. 9 m/s
C. 10 m/s
D. 11 m/s
Correct Answer: C. 10 m/s
Explanation:
The average speed of the runner is calculated by dividing the distance by the time. Therefore, the average speed is 300 meters / 30 seconds = 10 meters per second.

Question 71:
Topic: Percentages
Question: If a product’s original price is ₹1,000 and it is marked down by 30%, what is the sale price?
Options:
A. ₹650
B. ₹700
C. ₹750
D. ₹800
Correct Answer: B. ₹700
Explanation:
A 30% markdown means the price is reduced by 30% of the original price. 30% of ₹1,000 is ₹1,000 × 30/100 = ₹300. Therefore, the sale price is ₹1,000 – ₹300 = ₹700.

Question 72:
Topic: Arithmetic Aptitude
Question: What is 55% of 300?
Options:
A. 155
B. 165
C. 175
D. 185
Correct Answer: B. 165
Explanation:
55% of 300 is calculated as 300 × 55/100 = 165.

Question 73:
Topic: Data Interpretation
Question: A line graph shows a decrease in temperature from 25°C to 15°C. What is the percentage decrease in temperature?
Options:
A. 30%
B. 40%
C. 50%
D. 60%
Correct Answer: B. 40%
Explanation:
The decrease in temperature is 25°C – 15°C = 10°C. The percentage decrease is (10°C/25°C) × 100 = 40%.

Question 74:
Topic: Time and Speed
Question: A train travels 200 km in 2.5 hours. What is its average speed in km/h?
Options:
A. 75 km/h
B. 80 km/h
C. 85 km/h
D. 90 km/h
Correct Answer: B. 80 km/h
Explanation:
The average speed of the train is calculated by dividing the distance by the time. Therefore, the average speed is 200 km / 2.5 hours = 80 km/h.

Question 75:
Topic: Probability
Question: A box contains 8 black and 7 white balls. What is the probability of drawing a white ball?
Options:
A. 7/15
B. 8/15
C. 9/15
D. 10/15
Correct Answer: A. 7/15
Explanation:
There are 7 white balls out of a total of 15 (8 black + 7 white). Therefore, the probability of drawing a white ball is 7/15.

Question 76:
Topic: Pipes and Cisterns
Question: A pipe can fill a tank in 45 minutes, and another pipe can empty it in 60 minutes. If both pipes are opened together, will the tank get filled or emptied, and in how much time?
Options:
A. Filled in 180 minutes
B. Emptied in 180 minutes
C. Filled in 90 minutes
D. Emptied in 90 minutes
Correct Answer: B. Emptied in 180 minutes
Explanation:
The first pipe fills 1/45 of the tank per minute, and the second pipe empties 1/60 of the tank per minute. Together, they fill 1/45 – 1/60 = -1/180 of the tank per minute (negative value indicates emptying). Therefore, the tank will be emptied in 180 minutes.

Question 77:
Topic: Percentages
Question: If a person’s salary increases from ₹20,000 to ₹22,000, what is the percentage increase?
Options:
A. 8%
B. 10%
C. 12%
D. 15%
Correct Answer: B. 10%
Explanation:
The increase in salary is ₹22,000 – ₹20,000 = ₹2,000. The percentage increase is (₹2,000/₹20,000) × 100 = 10%.

Question 78:
Topic: Arithmetic Aptitude
Question: What is 35% of 400?
Options:
A. 130
B. 140
C. 150
D. 160
Correct Answer: B. 140
Explanation:
35% of 400 is calculated as 400 × 35/100 = 140.

Question 79:
Topic: Data Interpretation
Question: If a histogram shows that a factory produced 100 units in January and 120 units in February, what is the percentage increase in production?
Options:
A. 15%
B. 18%
C. 20%
D. 22%
Correct Answer: C. 20%
Explanation:
The increase in production is 120 units – 100 units = 20 units. The percentage increase is (20/100) × 100 = 20%.

Question 80:
Topic: Time and Speed
Question: A cyclist covers 150 km in 5 hours. What is her average speed in km/h?
Options:
A. 28 km/h
B. 30 km/h
C. 32 km/h
D. 35 km/h
Correct Answer: B. 30 km/h
Explanation:
The average speed of the cyclist is calculated by dividing the distance by the time. Therefore, the average speed is 150 km / 5 hours = 30 km/h.

Question 81:
Topic: Probability
Question: A bag contains 10 yellow and 5 green balls. What is the probability of drawing a green ball?
Options:
A. 1/3
B. 1/4
C. 1/5
D. 1/6
Correct Answer: A. 1/3
Explanation:
There are 5 green balls out of a total of 15 (10 yellow + 5 green). Therefore, the probability of drawing a green ball is 5/15 = 1/3.

Question 82:
Topic: Pipes and Cisterns
Question: Two pipes A and B can fill a tank in 30 minutes and 40 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?
Options:
A. 17 minutes
B. 18 minutes
C. 19 minutes
D. 20 minutes
Correct Answer: A. 17 minutes
Explanation:
Pipe A fills 1/30 of the tank per minute, and pipe B fills 1/40 of the tank per minute. Together, they fill 1/30 + 1/40 = 7/120 of the tank per minute. Therefore, it will take approximately 17 minutes to fill the tank.

Question 83:
Topic: Percentages
Question: A shirt priced at ₹800 is sold with a 25% discount. What is the sale price?
Options:
A. ₹550
B. ₹600
C. ₹650
D. ₹700
Correct Answer: B. ₹600
Explanation:
A 25% discount on ₹800 is ₹800 × 25/100 = ₹200. Therefore, the sale price is ₹800 – ₹200 = ₹600.

Question 84:
Topic: Arithmetic Aptitude
Question: What is 50% of 250?
Options:
A. 115
B. 125
C. 135
D. 145
Correct Answer: B. 125
Explanation:
50% of 250 is calculated as 250 × 50/100 = 125.

Question 85:
Topic: Data Interpretation
Question: A bar chart shows the number of books sold by a bookstore in each quarter. If 300 books were sold in the first quarter, and 360 in the second, what is the percentage increase in sales?
Options:
A. 15%
B. 18%
C. 20%
D. 22%
Correct Answer: C. 20%
Explanation:
The increase in sales is 360 books – 300 books = 60 books. The percentage increase is (60/300) × 100 = 20%.