General Quantitative Aptitude Basics Questions and Answers — Questions and Answers
Question 1: A shopkeeper sells an item for $150 after marking it up by 25% on the cost price. Due to low sales, he decides to offer a discount. What is the maximum percentage discount he can offer on the marked price to avoid making a loss?
- 15%
- 20% (Correct answer)
- 25%
- 30%
Correct answer: 20%
First, find the cost price (CP). The marked price ($150) is 125% of the CP. So, CP = $150 / 1.25 = $120. To avoid a loss, the selling price must not be less than the cost price ($120). The maximum discount is the difference between the marked price and the cost price, which is $150 - $120 = $30. The discount percentage is calculated on the marked price: ($30 / $150) * 100 = 20%.
Question 2: Working alone, machine A can complete a task in 6 hours. Working alone, machine B can complete the same task in 9 hours. If both machines start working together, but machine A breaks down after 2 hours, how many more hours will it take for machine B to complete the rest of the task alone?
- 3 hours
- 4.5 hours
- 5 hours
- 4 hours (Correct answer)
Correct answer: 4 hours
Machine A's 1-hour work rate is 1/6 of the task. Machine B's 1-hour work rate is 1/9 of the task. Together, their combined rate is 1/6 + 1/9 = 5/18 of the task per hour. In 2 hours, they complete 2 * (5/18) = 5/9 of the task. The remaining work is 1 - 5/9 = 4/9 of the task. Since only machine B is working, the time required is (Remaining Work) / (B's Rate) = (4/9) / (1/9) = 4 hours.
Question 3: The average age of a group of 30 students is 14 years. When the teacher's age is included, the average age of the group increases to 15 years. What is the teacher's age?
- 31 years
- 44 years
- 45 years (Correct answer)
- 59 years
Correct answer: 45 years
The total age of the 30 students is 30 * 14 = 420 years. When the teacher is included, there are 31 people in the group, and the new average age is 15. The new total age is 31 * 15 = 465 years. The teacher's age is the difference between the new total age and the original total age: 465 - 420 = 45 years.
Question 4: A train traveling at a constant speed of 90 km/hr crosses a stationary pole in 8 seconds. What is the length of the train?
- 180 meters
- 720 meters
- 200 meters (Correct answer)
- 250 meters
Correct answer: 200 meters
First, convert the speed from km/hr to m/s. Speed = 90 km/hr * (1000 m/km) / (3600 s/hr) = 25 m/s. The distance the train travels to cross a pole is equal to its own length. Using the formula Distance = Speed × Time, the length of the train is 25 m/s * 8 s = 200 meters.
Question 5: The salaries of two individuals, Alex and Ben, are in the ratio of 4:5. If Alex's salary is increased by 10% and Ben's salary is increased by 20%, what is the new ratio of their salaries?
- 4:6
- 11:15 (Correct answer)
- 5:7
- 22:25
Correct answer: 11:15
Let Alex's original salary be 4x and Ben's be 5x. After a 10% increase, Alex's new salary is 4x * 1.10 = 4.4x. After a 20% increase, Ben's new salary is 5x * 1.20 = 6.0x. The new ratio of their salaries is 4.4x : 6.0x. To remove the decimals, multiply both sides by 10, which gives 44:60. This ratio can be simplified by dividing both sides by their greatest common divisor, 4, resulting in the new ratio of 11:15.
Question 6: A sum of money is invested at a simple interest rate of 8% per annum. In how many years will the investment double itself?
- 8 years
- 10 years
- 12.5 years (Correct answer)
- 15 years
Correct answer: 12.5 years
For the investment to double, the total interest earned must be equal to the principal amount (P). The formula for simple interest is I = P * R * T, where I is interest, P is principal, R is the rate, and T is the time. We want I = P. So, P = P * 0.08 * T. Dividing both sides by P gives 1 = 0.08 * T. Therefore, T = 1 / 0.08 = 12.5 years.
General Quantitative Aptitude Basics Questions and Answers
A shopkeeper sells an item for $150 after marking it up by 25% on the cost price.
Due to low sales, he decides to offer a discount.
What is the maximum percentage discount he can offer on the marked price to avoid making a loss?