🔢 Quantitative Aptitude Questions with Solutions 2025 –by Planet E

📘 Introduction

Quantitative Aptitude is a vital section of any competitive management entrance exam. Strong problem-solving skills, conceptual clarity, and practice with high-difficulty questions are essential to master this section. At Planet E, we’ve curated 20 challenging questions across Arithmetic, Algebra, Geometry, and Modern Math to help aspirants prepare effectively for top-tier B-school entrance tests in 2025.

🔥 20 Quantitative Aptitude Questions with Detailed Solutions

✅ Arithmetic

1. A person spends 40% of his income on rent, 20% on food, and 10% on miscellaneous. If he still saves ₹12,000, what is his income?

Solution:
Expenses = 40% + 20% + 10% = 70%
Savings = 30%
So, 30% = ₹12,000 → 100% = ₹40,000
✅ Answer: ₹40,000

2. A train covers 150 km in 3 hours with stops. If the train hadn’t stopped, it could have maintained a speed of 60 km/hr. For how many minutes did it stop?

Solution:
Time without stop = 150/60 = 2.5 hours
Time taken = 3 hours
Stopping time = 0.5 hours = 30 minutes

✅ Answer: 30 minutes

3. A can complete a work in 12 days, B in 15 days. They work together for 3 days, and then A leaves. How long will B take to finish the remaining work?

Solution:
A’s 1 day work = 1/12, B’s = 1/15
In 3 days: A + B = 3 × (1/12 + 1/15) = 3 × (9/60) = 27/60
Remaining work = 1 – 27/60 = 33/60
B alone = 33/60 ÷ (1/15) = (33/60) × 15 = 8.25 days

✅ Answer: 8.25 days

4. A man can row 72 km downstream in 6 hours. If the speed of the stream is 2 km/h, find his speed in still water.

Solution:
Downstream speed = 72/6 = 12 km/h
Let speed in still water be x → x + 2 = 12 → x = 10 km/h

✅ Answer: 10 km/h

5. A shopkeeper marks an item 40% above cost and gives a discount of 20%. What is the profit percentage?

Solution:
Let CP = ₹100 → Marked Price = ₹140 → SP = ₹140 × 0.8 = ₹112
Profit = 112 – 100 = ₹12 → Profit% = 12%

✅ Answer: 12%

✅ Algebra

6. If x+1x=3x + \frac{1}{x} = 3x+x1​=3, then find x2+1x2x^2 + \frac{1}{x^2}x2+x21​

Solution:
Square both sides: x2+1×2+2=9x^2 + \frac{1}{x^2} + 2 = 9x2+x21​+2=9 → x2+1×2=7x^2 + \frac{1}{x^2} = 7x2+x21​=7

✅ Answer: 7

7. Solve for x: x2−7x+12=0x^2 – 7x + 12 = 0x2−7x+12=0

Solution:
Factorization: x2−3x−4x+12=0x^2 – 3x – 4x + 12 = 0x2−3x−4x+12=0 → $(x-3)(x-4)=0$

✅ Answer: x = 3 or 4

8. If $a+b=10$ and $ab=21$, find a2+b2a^2 + b^2a2+b2

Solution:
(a+b)2=a2+b2+2ab=100(a + b)^2 = a^2 + b^2 + 2ab = 100(a+b)2=a2+b2+2ab=100
→ a2+b2=100−42=58a^2 + b^2 = 100 – 42 = 58a2+b2=100−42=58

✅ Answer: 58

9. Find the value of x3+y3x+y\frac{x^3 + y^3}{x + y}x+yx3+y3​ if $x+y=10$ and $xy=21$

Solution:
Use identity: x3+y3=(x+y)3−3xy(x+y)x^3 + y^3 = (x + y)^3 – 3xy(x + y)x3+y3=(x+y)3−3xy(x+y)
= $1000-630=370$
→ Required value = 370 / 10 = 37

✅ Answer: 37

10. Find roots of the equation: 2×2−5x−3=02x^2 – 5x – 3 = 02x2−5x−3=0

Solution:
Using quadratic formula:
x = [5 ± √(25 + 24)] / 4 → x = [5 ± 7]/4 → x = 3, x = -0.5

✅ Answer: 3 or -0.5

✅ Geometry & Mensuration

11. Find the area of a triangle with base 10 cm and height 12 cm.

Solution:
Area = ½ × base × height = ½ × 10 × 12 = 60 cm²

✅ Answer: 60 cm²

12. A circle has a radius of 14 cm. Find its area.

Solution:
Area = πr² = 22/7 × 14 × 14 = 616 cm²

✅ Answer: 616 cm²

13. The perimeter of a rectangle is 60 cm and its length is 16 cm. Find its breadth.

Solution:
2(l + b) = 60 → l + b = 30 → b = 14

✅ Answer: 14 cm

14. A square has an area of 144 m². Find its perimeter.

Solution:
Side = √144 = 12 → Perimeter = 4 × 12 = 48 m

✅ Answer: 48 m

15. Find the length of the diagonal of a rectangle with sides 9 cm and 12 cm.

Solution:
Diagonal = √(9² + 12²) = √(81 + 144) = √225 = 15 cm

✅ Answer: 15 cm

✅ Modern Math & Number System

16. What is the LCM of 12, 15, and 20?

Solution:
Prime factors:
12 = 2² × 3, 15 = 3 × 5, 20 = 2² × 5 → LCM = 2² × 3 × 5 = 60

✅ Answer: 60

17. A number when divided by 7 leaves remainder 4. What is the remainder when the same number is divided by 14?

Solution:
Let number = 7k + 4. When divided by 14:
→ (7k + 4) mod 14
Try k = 1: 11, k = 2: 18 → remainder = 4 or 11 depending on k

✅ Answer: Cannot be determined without k

18. How many 3-digit numbers are divisible by 7?

Solution:
Smallest 3-digit = 105, largest = 994
→ Numbers = [(994 – 105)/7] + 1 = (889/7) + 1 = 127 + 1 = 128

✅ Answer: 128

19. What is the sum of the first 20 natural numbers?

Solution:
Sum = n(n+1)/2 = 20 × 21 / 2 = 210

✅ Answer: 210

20. A person borrows ₹12,000 at 10% compound interest annually. What will be the amount after 2 years?

Solution:
Amount = 12000 × (1 + 10/100)² = 12000 × 1.21 = ₹14,520

✅ Answer: ₹14,520

🎯 How to Master Quantitative Aptitude?

1. Focus on Conceptual Clarity – Build strong fundamentals.

2. Practice Daily – 10–15 quality questions per topic.

3. Take Timed Sectionals – Build speed and accuracy.

4. Use Data Analysis – Review past mock performance.

5. Join Planet E Coaching – Learn from 99+ %ilers.

🏁 Final Words from Planet E

Mastering advanced-level quantitative aptitude takes consistent practice, accurate problem solving, and expert guidance. Whether you’re preparing online or offline, Planet E offers premium coaching programs to boost your confidence and results. Start today and aim for the top!