The “Top 15 Arithmetic MCQs for Odisha Police Constable Exam” covers essential mathematical concepts critical for competitive exam preparation. This set includes questions from various topics such as Pipe & Cistern, Number System, Time & Work, Simple Interest (SI) & Compound Interest (CI), Calendar Days Calculation, Profit & Loss, Simplification, Probability, Time & Distance, Mensuration, LCM & HCF, and Boat & Stream. Each question is crafted to challenge candidates’ problem-solving skills and enhance their arithmetic proficiency. These MCQs offer a comprehensive approach to mastering key topics, providing step-by-step solutions and detailed explanations to aid in exam readiness.
Top 15 Arithmetic MCQs For Odisha Police Constable
- If x is a positive integer such that {3x + 5}/{7} is an integer, what is the smallest possible value of x?
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (d) 4
Solution: Let frac{3x + 5}/{7} = k, where k is an integer. Thus, 3x+5=7k. Rearranging, 3x=7k−5. For x to be an integer, 7k−5 must be divisible by 3. Trying successive values of k, the smallest k that satisfies this condition is k=3. Substituting, 3x=21−5, so x=16/3. Trying the next k=4, 3x=28−5=23, so x=23. Finally, trying k=5,3x=35−5=30, so x=10. Hence, the smallest x is 10. - A man spends 40% of his monthly salary on rent, 25% on food, and 15% on transportation. If he saves ₹9,000, what is his total monthly salary?
(a) ₹30,000
(b) ₹36,000
(c) ₹40,000
(d) ₹45,000
Ans: (b) ₹36,000
Solution: Let the monthly salary be S. He spends 40%+25%+15%=80% of his salary, so he saves 100%−80%=20%. If 20%of the salary is ₹9,000, then 100% of the salary is (9,000×100)/20=₹45,000 - The average of 5 numbers is 15. If two of the numbers are 10 and 20, what is the average of the remaining 3 numbers?
(a) 10
(b) 12
(c) 15
(d) 20
Ans: (a) 10
Solution: Solution: The sum of the 5 numbers is 5×15=75. The sum of the first two numbers is 10+20=30. Thus, the sum of the remaining 3 numbers is 75−30=45. Therefore, the average of the remaining 3 numbers is 45/3 =15.5. - A sum of money doubles in 5 years at simple interest. What is the rate of interest per annum?
(a) 10%
(b) 20%
(c) 15%
(d) 25%
Ans: (b) 20%
Solution: Solution: Let the principal be 𝑃 and the rate of interest be r%. In 5 years, the amount is 2P, and the simple interest is P. Simple interest formula is SI=(P×r×t)/100
Thus, P= (P×r×t)/100 , so 𝑟=100/5=20%. - A train travels from point A to point B in 3 hours at a speed of 60 km/hr. If it travels from B to A at a speed of 90 km/hr, what is the average speed of the train for the entire journey?
(a) 72 km/hr
(b) 75 km/hr
(c) 80 km/hr
(d) 85 km/hr
Ans: (a) 72 km/hr
Solution: The distance between A and B is 60×3=180 km. Time taken from B to A is 180/90=2 hours. Total distance for the round trip is 180+180=360 km, and total time is 3+2=5 hours. Average speed is 360/5=72 km/hr.. - The sum of the squares of two consecutive odd numbers is 410. What are the numbers?
(a) 9 and 11
(b) 11 and 13
(c) 13 and 15
(d) 15 and 17
Ans: (b) 11 and 13
Solution: Let the odd numbers be x and x+2. Then, x^2 + (x+2)^2 = =410. Expanding and solving: x^2 + x^2 + 4x + 4 = 410, x^2 + 4x + 4 = 410, 2x^2 + 4x = 406, x^2 + 2x = 203=0. Solving x^2 + 2x – 203 =0,(x−11)(x+13)=0, x=11. Therefore, the numbers are 11 and 13. - If a car covers 180 km in 3 hours and another car covers 240 km in 4 hours, what is the ratio of their speeds?
(a) 3:4
(b) 4:3
(c) 2:3
(d) 3:2
Ans: (b) 4:3
Solution: Speed of the first car is 180/3 =60 km/hr. Speed of the second car is 240/4 =60 km/hr. The ratio of the speeds is 60/60=1:1. - A man buys a watch at a discount of 25% on the marked price. If he sells it for ₹9000, what was the marked price?
(a) ₹10,000
(b) ₹12,000
(c) ₹13,500
(d) ₹15,000
Ans: (a) ₹12,000
Solution: Let the marked price be 𝑀. After a 25% discount, the selling price is 75% of 𝑀 =0.75M=9000, hence M= 9000/0.75 =12000. - The sum of three consecutive integers is 69. What are the integers?
(a) 22, 23, 24
(b) 21, 22, 23
(c) 23, 24, 25
(d) 20, 21, 22
Ans: (b) 21, 22, 23
Solution: Let the integers be x−1, x, and x+1. Then,
(x−1)+x+(x+1)=69, 3x=69, x=23. Hence, the integers are 22, 23, and 24. - A student scores 85, 90, and 80 in three subjects. If the average score needs to be 88 for the fourth subject, what must be the score in the fourth subject?
(a) 95
(b) 96
(c) 97
(d) 98
Ans: (a) 95
Solution: Let the score in the fourth subject be x.
The average score is 85+90+80+x =88.
Solving for 255+x=352,
x=352−255=97. - A man buys 4 pens for ₹40 and sells them at a price of ₹12 each. What is his profit percentage?
(a) 20%
(b) 25%
(c) 30%
(d) 35%
Ans: (b) 25%
Solution: Cost price of 4 pens = ₹40,
hence cost price of 1 pen = ₹10. Selling price of 1 pen = ₹12. Profit per pen = ₹12 – ₹10 = ₹2.
Total profit = ₹2 times 4 = ₹8.
Total cost price = ₹40.
Profit percentage = 8/40×100=20% - A shopkeeper increases the price of an item by 25% and then gives a 10% discount. What is the effective percentage increase in the price of the item?
(a) 10%
(b) 15%
(c) 12.5%
(d) 20%
Ans: (c) 12.5%
Solution: Let the original price be ₹100. After a 25% increase, the new price is ₹125. After a 10% discount on ₹125, the selling price is 125×(1−0.10)=125×0.90=112.5. The effective increase is 112.5−100= 12.5.
Percentage increase =12.5/100×100=12.5%. - A student scores 70, 75, 80, and 85 in four tests. If the scores are to be in arithmetic progression, what is the score of the fifth test if the average score of all five tests is 80?
(a) 90
(b) 85
(c) 95
(d) 100
Ans: (a) 90
Solution: The sum of the five scores = 80×5=400.
The sum of the first four scores = 70+75+80+85=310.
Hence, the score of the fifth test =
400−310=90. - A man borrows ₹10,000 at 8% per annum compound interest. What is the amount he will have to pay after 2 years?
(a) ₹11,664
(b) ₹11,600
(c) ₹11,680
(d) ₹11,760
Ans: (a) ₹11,664
Solution: Amount
𝐴=𝑃(1+𝑟/100)^𝑡
Here,
P=10,000,
r=8%, and
t=2. Thus,
A=10,000(1+8/100)^8
=10,000(1.08)^2
=10,000×1.1664=11,664. - A person buys an article for ₹720 and sells it at a profit of 20%. What is the selling price?
(a) ₹864
(b) ₹840
(c) ₹900
(d) ₹880
Ans: (a) ₹864
Solution: Selling price = 720×(1+0.20)=720×1.20=₹864.
