Here are 10 aptitude-based questions along with their answers and explanations:
Question 1:
A train travels a distance of 300 km at a constant speed. If the speed of the train is increased by 20 km/hr, it would take 2 hours less to cover the same distance. Find the original speed of the train.
Answer:
Let the original speed of the train be x km/hr. According to the given information, (300/x) - (300/(x+20)) = 2. Solving this equation, we get x = 60 km/hr.
Explanation:
To solve this question, we can use the concept of relative speed. The difference in time taken by the train at different speeds is given as 2 hours. By setting up the equation and solving for the speed, we can find the original speed of the train.
Question 2:
If the ratio of the ages of A and B is 3:4 and the sum of their ages is 28 years, find the age of B.
Answer:
Let the ages of A and B be 3x and 4x respectively. According to the given information, 3x + 4x = 28.
Solving this equation, we get x = 4. Therefore, the age of B is 4x = 4 * 4 = 16 years.
Explanation:
In this question, we are given the ratio of the ages of two individuals and the sum of their ages. By setting up the equation and solving for the unknown variable, we can find the age of B.
Question 3:
In a class, there are 40 boys and 30 girls. If the average weight of boys is 60 kg and the average weight of girls is 50 kg, find the average weight of the whole class.
Answer:
The total weight of boys = 40 * 60 = 2400 kg.
The total weight of girls = 30 * 50 = 1500 kg.
The total weight of the class = 2400 + 1500 = 3900 kg.
The average weight of the class = 3900 / (40 + 30) = 65 kg.
Explanation:
To find the average weight of the whole class, we need to calculate the total weight of all the individuals and then divide it by the total number of individuals. By summing up the weights of boys and girls separately and then dividing by the total number of students, we can find the average weight of the class.
Question 4:
The selling price of an article is 20% more than its cost price. Find the profit percentage.
Answer:
Let the cost price of the article be C. The selling price of the article is 120% of the cost price, which is 1.2C.
Profit percentage = (Selling price - Cost price) / Cost price * 100 = (1.2C - C) / C * 100 = 20%.
Explanation:
To find the profit percentage, we need to calculate the difference between the selling price and the cost price, divide it by the cost price, and then multiply by 100 to express it as a percentage. In this question, the selling price is given as 20% more than the cost price, which results in a profit percentage of 20%.
Question 5:
A box contains 6 red balls and 4 green balls. If two balls are drawn at random, what is the probability of getting both balls of the same color?
Answer:
Total number of balls = 6 red + 4 green = 10.
Probability of drawing a red ball in the first draw = 6/10.
Probability of drawing a red ball in the second draw (without replacement) = 5/9.
Probability of drawing both balls of the same color = (6/10) * (5/9) = 1/3.
Explanation:
To find the probability of drawing two balls of the same color, we need to calculate the probability of drawing a ball of a specific color in the first draw and the probability of drawing a ball of the same color in the second draw (assuming no replacement). By multiplying these probabilities, we can find the probability of getting both balls of the same color.
Question 6:
A sum of money becomes double in 5 years at a certain rate of simple interest. Find the rate of interest.
Answer:
Let the principal amount be P. According to the given information, P + (P * R * 5/100) = 2P.
Simplifying this equation, we get R = 20%.
Explanation:
To find the rate of interest, we can use the formula for simple interest. The principal amount is multiplied by the rate of interest, and time, and divided by 100. By setting up the equation and solving for the rate of interest, we can find the required answer.
Question 7:
If the sum of the digits of a two-digit number is 8 and the difference between the digits is 2, find the number.
Answer:
Let the tens digit be x and the units digit be y. According to the given information, x + y = 8 and x - y = 2.
Solving these equations, we get x = 5 and y = 3. Therefore, the number is 53.
Explanation:
In this question, we are given the sum and difference of the digits of a two-digit number. By setting up the equations based on the given information and solving for the variables, we can determine the values of the digits and find the number.
Question 8:
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is drawn at random, what is the probability of getting a blue ball?
Answer:
Total number of balls = 5 red + 3 blue + 2 green = 10.
Probability of getting a blue ball = 3/10.
Explanation:
To find the probability of getting a blue ball, we need to calculate the number of favorable outcomes (in this case, the number of blue balls) and divide it by the total number of possible outcomes (the total number of balls in the bag).
Question 9:
The population of the town is 20,000. If the population increases by 10% in the first year and decreases by 5% in the second year, find the population after two years.
Answer:
Population after the first year = 20,000 + (20,000 * 10/100) = 22,000.
Population after the second year = 22,000 - (22,000 * 5/100) = 20,900.
Explanation:
To calculate the population after two years, we need to apply the percentage changes successively. In this case, the population increases by 10% in the first year and decreases by 5% in the second year. By performing the calculations step by step, we can find the population after two years.
Question 10:
A car travels a distance of 360 km at a speed of 60 km/hr. How much time does it take to cover the distance?
Answer:
Time = Distance / Speed = 360 km / 60 km/hr = 6 hours.
Explanation:
To find the time taken to cover a distance, we need to divide the distance by the speed. In this question, the distance is given as 360 km and the speed is given as 60 km/hr. By performing the division, we can find the required time in hours.
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