10 Aptitude-Based Questions with Detailed Answers and Explanations for Skill Enhancement

Question 1:

A train travels at a speed of 80 km/h for a certain distance. If the speed is reduced by 20 km/h, it would take 1 hour more to cover the same distance. Find the distance covered by the train.

Answer: 400 km

Explanation: Let the distance covered by the train be 'd' km. Using the formula Time = Distance / Speed, we can form the equation: d / 80 = d / 60 + 1. Solving this equation, we find d = 400 km.

Question 2:

A merchant bought a product for Rs. 500 and sold it for Rs. 600. What is the percentage profit?

Answer: 20%

Explanation: Profit percentage is calculated using the formula: (Profit / Cost Price) * 100. Here, the profit is Rs. 100 and the cost price is Rs. 500. So, the profit percentage is (100 / 500) * 100 = 20%.

Question 3:

If the price of a product is increased by 20%, by how much percent should it be reduced to bring it back to the original price?

Answer: 16.67%

Explanation: Let the original price be 100. After a 20% increase, the price becomes 120. To bring it back to the original price of 100, we need to reduce it by (20 / 120) * 100 ≈ 16.67%.

Question 4:

A train completes a journey in 4 hours at an average speed of 60 km/h. If the train had traveled at a speed of 80 km/h, how much time would it have taken to complete the same journey?

Answer: 3 hours

Explanation: Time is inversely proportional to speed. So, if the speed is increased, the time taken to cover the same distance decreases. In this case, the ratio of speeds is 80:60, which is equivalent to 4:3. Therefore, the time taken at a speed of 80 km/h would be (4 / 3) * 4 = 3 hours.

Question 5:

A sum of money invested at 10% compound interest per annum becomes Rs. 1210 in 2 years. What would be the sum if the interest is compounded annually for 3 years at the same rate?

Answer: Rs. 1331

Explanation: Compound interest is calculated using the formula: A = P * (1 + r/n)^(nt), where A is the final amount, P is the principal, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time in years. In this case, P * (1 + 10/100)^(2*1) = 1210. Solving for P, we get P = 1100. Now, substituting the values in the formula for 3 years, we have P * (1 + 10/100)^(1*3) = 1331.

Question 6:

If x^2 - 5x + 6 = 0, find the value of x.

Answer: x = 2 or x = 3

Explanation: The given equation can be factored as (x - 2)(x - 3) = 0. Setting each factor equal to zero, we get x - 2 = 0 or x - 3 = 0, which leads to x = 2 or x = 3.

Question 7:

If a number is increased by 25% and then decreased by 20%, what is the net percentage change?

Answer: 4% increase

Explanation: Let the original number be 100. After a 25% increase, the number becomes 125. Then, after a 20% decrease, the number becomes (80/100) * 125 = 100. The net change is 100 - 100 = 0, which means there is no change. However, in terms of percentage, the final number is 4% greater than the original number.

Question 8:

A car covers a distance of 360 km in 6 hours. If it continues to travel at the same speed, how long will it take to cover a distance of 480 km?

Answer: 8 hours

Explanation: The speed of the car is calculated as distance divided by time. So, the speed of the car is 360 km / 6 hours = 60 km/h. To cover a distance of 480 km at the same speed, it will take 480 km / 60 km/h = 8 hours.

Question 9:

If the ratio of boys to girls in a class is 3:5 and the total number of students is 80, how many boys are there?

Answer: 24 boys

Explanation: The ratio of boys to girls is given as 3:5, which means for every 3 boys, there are 5 girls. The total ratio is 3 + 5 = 8. So, we can set up a proportion: 3/8 = x/80. Solving for x, we get x = (3/8) * 80 = 24 boys.

Question 10:

The sum of the two numbers is 80. If one number is twice the other, find the numbers.

Answer: The numbers are 32 and 48.

Explanation: Let one number be x. The other number is then 2x. According to the given condition, x + 2x = 80. Solving this equation, we get x = 32. Therefore, the numbers are 32 and 48.

These aptitude questions cover various concepts and can help you enhance your problem-solving skills. Understanding the explanations will provide you with the necessary insights to solve similar questions in the future.