# Quantitative Aptitude Questions with Answers

12 quantitative questions of the kind Indian placement tests set, each with the correct option and a step-by-step solution.

_Source: Astra (https://useastra.in). Updated 2026-09-05._

### 1. A man's salary is increased by 20%. If his new salary is INR 30,000, what was his original salary before the increase was applied?

A. INR 24,000
B. INR 25,000
C. INR 25,500
D. INR 36,000

**Answer:** B

**Solution:** Let the original salary be 'S'. The salary was increased by 20%, so the new salary is S + (0.20 * S), which equals 1.20 * S. We are given that the new salary is INR 30,000. So, we set up the equation: 1.20 * S = INR 30,000. To find S, we divide INR 30,000 by 1.20. S = INR 30,000 / 1.2. This calculation gives S = INR 25,000. Therefore, the man's original salary was INR 25,000. You can verify this by calculating 20% of INR 25,000 (which is INR 5,000) and adding it back, which correctly results in INR 30,000.

### 2. A and B together can complete a piece of work in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 30 days. How many days will A take to complete the task alone?

A. 24 days
B. 40 days
C. 48 days
D. 60 days

**Answer:** B

**Solution:** To solve this, we find the one-day work (efficiency) for each pair. (A + B)'s 1-day work = 1/20. (B + C)'s 1-day work = 1/30. (A + C)'s 1-day work = 1/30. First, add all three equations together: 2(A + B + C)'s 1-day work = (1/20) + (1/30) + (1/30). 2(A + B + C) = (3 + 2 + 2) / 60 = 7/60. (A + B + C)'s 1-day work = 7/120. Now, we just need to find A's 1-day work. We can do this by subtracting (B + C)'s work from the total: A's 1-day work = (A + B + C) - (B + C) = (7/120) - (1/30). To subtract, find a common denominator: (7/120) - (4/120) = 3/120. A's 1-day work is 3/120, which simplifies to 1/40. If A does 1/40th of the work per day, A will take 40 days to complete the task alone.

### 3. A shopkeeper sells an article for INR 450, making a profit of 25%. At what price should he sell the article to make a loss of 10%?

A. INR 315
B. INR 324
C. INR 360
D. INR 405

**Answer:** B

**Solution:** First, we must find the Cost Price (CP). We know the Selling Price (SP) is INR 450 and the profit is 25%. The formula is SP = CP * (1 + Profit%). So, INR 450 = CP * (1 + 0.25), which means INR 450 = CP * 1.25. To find the CP, divide INR 450 by 1.25. CP = INR 450 / 1.25 = INR 360. So, the cost price of the article is INR 360. Now, the shopkeeper wants to sell it at a loss of 10%. The new SP will be CP * (1 - Loss%). New SP = INR 360 * (1 - 0.10) = INR 360 * 0.90. Calculating this, New SP = INR 324. Therefore, he should sell the article for INR 324 to make a 10% loss.

### 4. A train running at a speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train in meters?

A. 90 m
B. 135 m
C. 150 m
D. 540 m

**Answer:** C

**Solution:** First, convert the speed from km/hr to m/s. The conversion factor is 5/18. Speed = 60 * (5/18) m/s = 10 * (5/3) m/s = 50/3 m/s. The time taken to cross the pole is 9 seconds. When a train crosses a pole (or a stationary man), the distance it travels is equal to its own length. Therefore, Length of Train = Speed * Time. Length = (50/3 m/s) * 9 s. The 's' units cancel out. Length = 50 * (9/3) m = 50 * 3 m = 150 meters. The length of the train is 150 meters. This problem is fundamental for understanding relative speed and unit consistency.

### 5. Find the simple interest on INR 5,000 for 3 years at a rate of 8% per annum. How does this compare to the amount at maturity?

A. INR 400
B. INR 1,200
C. INR 1,320
D. INR 6,200

**Answer:** B

**Solution:** The formula for Simple Interest (SI) is: SI = (P * R * T) / 100, where P is the Principal, R is the Rate of interest per annum, and T is the Time in years. Here, P = INR 5,000, R = 8%, and T = 3 years. SI = (5000 * 8 * 3) / 100. SI = 50 * 8 * 3. SI = 400 * 3 = INR 1,200. So, the simple interest earned is INR 1,200. The question also asks how this compares to the amount at maturity. The amount at maturity (A) is the Principal + Simple Interest. A = P + SI. A = INR 5,000 + INR 1,200 = INR 6,200. The interest (INR 1,200) is the profit earned on the principal (INR 5,000), resulting in a total maturity value of INR 6,200.

### 6. What is the compound interest on INR 10,000 for 2 years at 10% per annum, compounded annually?

A. INR 2,000
B. INR 2,100
C. INR 2,210
D. INR 1,210

**Answer:** B

**Solution:** To calculate Compound Interest (CI), we first find the total Amount (A) using the formula: A = P * (1 + R/n)^(n*t), where P=INR 10,000, R=0.10, t=2 years, and n=1 (compounded annually). A = 10000 * (1 + 0.10/1)^(1*2). A = 10000 * (1.10)^2. A = 10000 * 1.21 = INR 12,100. This INR 12,100 is the total amount. The Compound Interest is the total amount minus the original principal. CI = A - P. CI = INR 12,100 - INR 10,000 = INR 2,100. Alternatively, for 2 years: Year 1 Interest = 10% of INR 10,000 = INR 1,000. New Principal for Year 2 = INR 11,000. Year 2 Interest = 10% of INR 11,000 = INR 1,100. Total CI = INR 1,000 + INR 1,100 = INR 2,100.

### 7. Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new ratio becomes 12:23. What is the smaller number?

A. 11
B. 22
C. 33
D. 55

**Answer:** C

**Solution:** Let the two numbers be 3x and 5x. According to the problem, if 9 is subtracted from each number, the new ratio becomes 12:23. This can be written as an equation: (3x - 9) / (5x - 9) = 12 / 23. To solve for x, we cross-multiply: 23 * (3x - 9) = 12 * (5x - 9). 69x - 207 = 60x - 108. Now, group the x terms on one side and the constant terms on the other. 69x - 60x = 207 - 108. 9x = 99. x = 11. The question asks for the *smaller number*. The original numbers were 3x and 5x. The smaller number is 3x. Smaller number = 3 * 11 = 33. The larger number is 5 * 11 = 55.

### 8. The average age of a class of 30 students is 15 years. If the teacher's age is included, the average age increases by 1 year. What is the teacher's age?

A. 16 years
B. 30 years
C. 45 years
D. 46 years

**Answer:** D

**Solution:** First, find the total age of the 30 students. Total Age (Students) = Average * Number of Students = 15 * 30 = 450 years. When the teacher is included, the number of people becomes 31 (30 students + 1 teacher). The new average age increases by 1, so it becomes 15 + 1 = 16 years. Now, find the new total age including the teacher. Total Age (Students + Teacher) = New Average * New Number of People = 16 * 31 = 496 years. The teacher's age is the difference between the new total age and the original total age of the students. Teacher's Age = 496 - 450 = 46 years. Therefore, the teacher is 46 years old.

### 9. A jar contains a mixture of two liquids, A and B, in the ratio 4:1. When 10 liters of the mixture are removed and replaced with 10 liters of liquid B, the ratio becomes 2:3. What was the initial quantity of liquid A in the jar?

A. 4 liters
B. 8 liters
C. 16 liters
D. 20 liters

**Answer:** C

**Solution:** Let the initial quantities of A and B be 4x and 1x, making the total mixture 5x. When 10 liters of the mixture are removed, the liquids are removed in the same ratio (4:1). Amount of A removed = (4/5) * 10 = 8 liters. Amount of B removed = (1/5) * 10 = 2 liters. The new quantities are: A = 4x - 8, B = 1x - 2. Now, 10 liters of liquid B are added. The final quantities are: A = 4x - 8, B = (1x - 2) + 10 = 1x + 8. The new ratio is 2:3. So, (4x - 8) / (1x + 8) = 2 / 3. Cross-multiply: 3 * (4x - 8) = 2 * (1x + 8). 12x - 24 = 2x + 16. 10x = 40. x = 4. The question asks for the *initial quantity of liquid A*. Initial A = 4x = 4 * 4 = 16 liters.

### 10. A bag contains 3 red balls, 5 blue balls, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both balls are blue?

A. 1/9
B. 2/9
C. 4/9
D. 1/2

**Answer:** B

**Solution:** First, find the total number of balls in the bag. Total Balls = 3 (Red) + 5 (Blue) + 2 (Green) = 10 balls. We are drawing two balls *without replacement*. We want the probability that both are blue. Probability of the 1st ball being blue = (Number of Blue Balls) / (Total Balls) = 5 / 10. After drawing one blue ball, there are now 9 balls left in the bag, and only 4 of them are blue. Probability of the 2nd ball being blue (given the 1st was blue) = 4 / 9. To find the probability of *both* events happening, we multiply their probabilities: P(Both Blue) = P(1st Blue) * P(2nd Blue) = (5 / 10) * (4 / 9). P(Both Blue) = (1 / 2) * (4 / 9) = 4 / 18, which simplifies to 2/9. The probability of drawing two blue balls without replacement is 2/9.

### 11. What is 25% of 300?

A. 60
B. 75
C. 90
D. 120

**Answer:** B

**Solution:** To find 25% of 300, you can convert 25% to a fraction or a decimal. As a fraction, 25% = 25/100 = 1/4. So, the problem becomes (1/4) * 300 = 75. Alternatively, as a decimal, 25% = 0.25. So, the problem becomes 0.25 * 300. You can calculate this as (25 * 300) / 100 = 7500 / 100 = 75. Both methods give the same result. This is a foundational concept in aptitude, representing a quarter of the total value.

### 12. If a shirt costs INR 50 and is sold for INR 60, what is the profit percentage?

A. 10%
B. 16.67%
C. 20%
D. 25%

**Answer:** C

**Solution:** First, calculate the profit in dollars. Profit = Selling Price (SP) - Cost Price (CP). Profit = INR 60 - INR 50 = INR 10. Next, calculate the profit percentage. The profit percentage is *always* calculated based on the Cost Price (CP). The formula is (Profit / CP) * 100. Profit Percentage = (INR 10 / INR 50) * 100. This simplifies to (1/5) * 100 = 20%. Therefore, the shopkeeper made a 20% profit on the shirt. This calculation is crucial for understanding margins and business performance.

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