Preparing for competitive exams like the OSSSC PEO (Panchayat Executive Officer) and Odisha Police Constable requires speed, accuracy, and strong fundamentals in quantitative aptitude.
To help you test your preparation, we have extracted 20 essential mathematics practice questions covering key topics—including Arithmetic, Percentages, Ratios, Ages, Geometry, and Mensuration—accompanied by step-by-step solutions and answers.
1. Two numbers are in the ratio of 5:7. If 6 is added to each number, the ratio becomes 3:4. What are the two numbers?
Let the numbers be 5x and 7x. Then (5x + 6)/(7x + 6) = 3/4, giving x = 6. Therefore, the numbers are 30 and 42.
2. A can finish a work in 18 days. B is twice as efficient as A. If they work together, in how many days will the work be completed?
A’s daily work is 1/18 and B’s is 1/9. Their combined daily work is 1/6, so the work takes 6 days.
3. The ratio of the present ages of Amit and Rakesh is 7:5. Amit will be 36 years old after 8 years. How old is Rakesh now?
Amit’s present age is 36 – 8 = 28 years. Since 7 parts equal 28, one part is 4 years. Rakesh is 5 × 4 = 20 years old.
4. At what rate of Simple Interest per annum will a principal amount of ₹6,000 yield an interest of ₹12,000 in 5 years?
Using SI = (P × R × T)/100, we get 12,000 = (6,000 × R × 5)/100, giving R = 40%.
5. A cistern is normally filled in 6 hours, but it takes 3 hours longer to fill because of a leak at the bottom. How long will the leak take to empty a full cistern?
The normal filling rate is 1/6 and the rate with the leak is 1/9. Thus, the leak rate is 1/6 – 1/9 = 1/18, so it takes 18 hours to empty the cistern.
6. An article is sold at a 10% discount on its marked price of ₹3,840, giving a profit of 8%. If no discount were given, what would be the gain percentage?
The discounted selling price is ₹3,456. Since this represents 108% of the cost price, the cost price is ₹3,200. Selling at ₹3,840 gives a profit of ₹640, or 20%.
7. If the area of a triangle is 250 m² and the ratio of its base to its height is 4:5, what is the height of the triangle?
Let the base be 4x and height be 5x. Then area = 1/2 × 4x × 5x = 10x² = 250, so x = 5. Hence the height is 25 m.
8. A boatman goes 6 km upstream in a river where the speed of the current is 3 km/h. If his speed in still water is 6 km/h, how long will the upstream trip take?
Upstream speed = 6 – 3 = 3 km/h. Therefore, time = 6/3 = 2 hours.
9. The volume of a cube is 512 cm³. What is its total surface area?
The side of the cube is ∛512 = 8 cm. Total surface area = 6 × 8² = 384 cm².
10. The average age of 10 students and their teacher is 20 years. If the teacher’s age is excluded, the average age decreases by 2 years. What is the teacher’s age?
The total age of 11 people is 220 years. The total age of the 10 students is 10 × 18 = 180 years. Therefore, the teacher’s age is 40 years.
11. At what annual percentage rate will a sum of ₹500 amount to ₹864 in 3 years when compounded annually?
Using A = P(1 + R/100)^3, we get 864/500 = (6/5)^3. Therefore, 1 + R/100 = 6/5, giving R = 20%.
12. If the length of a rectangle is increased by 25% while the breadth remains unchanged, by what percentage does the area increase?
Since area = length × breadth and the breadth remains constant, a 25% increase in length causes a 25% increase in area.
13. Find the missing number in the following series: 5, 11, 19, 29, …
The differences are +6, +8 and +10. The next difference is +12, so the missing number is 29 + 12 = 41.
14. A starts a business with an investment of ₹2,500. Seven months later, B joins A as a partner. After one year, profits are divided in the ratio 3:4. How much did B contribute?
A invests ₹2,500 for 12 months, while B invests for 5 months. Using 2,500 × 12 : B × 5 = 3 : 4 gives B = ₹8,000.
15. A solid piece of iron of dimensions 44 cm × 42 cm × 21 cm is melted and recast into a solid sphere. What is the radius of the sphere? (π = 22/7)
Equating the cuboid volume to the sphere volume gives r³ = 9261. Therefore, r = 21 cm.
16. If a:b = 3:2, find the value of (5a – 2b) : (a + 3b).
Let a = 3 and b = 2. Then 5a – 2b = 11 and a + 3b = 9. Hence the ratio is 11:9.
17. What is the sum of the series 40 + 39 + 38 + … + 11?
There are 30 terms. Sum = 30/2 × (40 + 11) = 15 × 51 = 765.
18. A, B, and C start running around a circular track 12 km long from the same point and in the same direction at speeds of 4 km/h, 3 km/h, and 2 km/h respectively. After how many hours will they meet again at the starting point?
Their lap times are 3, 4 and 6 hours respectively. The LCM of 3, 4 and 6 is 12 hours.
19. If a:b = 7:9 and b:c = 5:7, what is the ratio of a:c?
a/c = (a/b) × (b/c) = (7/9) × (5/7) = 5/9. Therefore, a:c = 5:9.
20. Find the difference between simple interest and compound interest on ₹9,000 for 1 year at 6% per annum compounded half-yearly.
Simple interest is ₹540. Half-yearly compound interest is ₹548.10. Therefore, the difference is ₹8.10.
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