About a quarter of the Police Bharti written paper is arithmetic (official per-subject marks are not announced). The questions are basic, so speed is everything: learn the formula, then practise. The paper is in Marathi, so the Marathi term is given with each topic.
1. Simplification – BODMAS (सरळरूप)
Order: Brackets → Of → Division → Multiplication → Addition → Subtraction (division and multiplication left to right).
- Example: 36 ÷ 4 × 3 + 10 − 2 = 9 × 3 + 10 − 2 = 27 + 10 − 2 = 35.
- Example: 5 + 3 × (8 − 2) = 5 + 3 × 6 = 5 + 18 = 23.
2. LCM and HCF (लसावि – मसावि)
- HCF = biggest number that divides all the given numbers. LCM = smallest number that all the given numbers divide.
- For two numbers: LCM × HCF = product of the two numbers.
- Example: 12 = 2 × 2 × 3, 18 = 2 × 3 × 3 → HCF = 2 × 3 = 6, LCM = 2 × 2 × 3 × 3 = 36. Check: 6 × 36 = 216 = 12 × 18 ✔
- “Bells ring together again after…” type questions → LCM. “Biggest equal pieces/rows” → HCF.
3. Percentage (शेकडेवारी)
- x% of N = N × x/100. Useful: 50% = ½, 25% = ¼, 20% = 1/5, 12.5% = 1/8, 10% = 1/10.
- Increase by x%: new = old × (100 + x)/100. Decrease by x%: new = old × (100 − x)/100.
- Example: A salary of ₹18,000 increases by 15%. New salary = 18,000 × 115/100 = ₹20,700.
- Example: 30 is what % of 120? → 30/120 × 100 = 25%.
4. Profit and loss (नफा – तोटा)
- Profit = SP − CP; Loss = CP − SP (CP = cost price/खरेदी किंमत, SP = selling price/विक्री किंमत).
- Profit % = Profit/CP × 100; Loss % = Loss/CP × 100 (always on CP).
- SP = CP × (100 + profit%)/100.
- Example: A cycle bought for ₹2,400 is sold at 10% loss. SP = 2,400 × 90/100 = ₹2,160.
- Discount (सूट) is on the marked price: SP = MP × (100 − discount%)/100.
5. Simple and compound interest (सरळव्याज – चक्रवाढ व्याज)
- Simple interest: SI = P × R × T / 100 (P = principal/मुद्दल, R = rate % per year, T = years). Amount = P + SI.
- Compound interest: A = P × (1 + R/100)ᵀ, CI = A − P.
- Example (SI): ₹6,000 at 9% for 2 years → 6,000 × 9 × 2/100 = ₹1,080.
- Example (CI): ₹8,000 at 5% for 2 years → A = 8,000 × 1.05 × 1.05 = ₹8,820 → CI = ₹820.
- Shortcut: for 2 years, CI − SI = P × (R/100)². Here 8,000 × (5/100)² = ₹20 (SI = ₹800, CI = ₹820 ✔).
6. Ratio, proportion and partnership (गुणोत्तर – प्रमाण)
- Divide amount S in ratio a : b → first share = S × a/(a + b), second = S × b/(a + b).
- In a proportion a : b = c : d, product of extremes = product of means (a × d = b × c).
- Example: ₹2,100 shared in the ratio 3 : 4 → ₹900 and ₹1,200.
7. Average (सरासरी)
- Average = sum of the values / number of values.
- Example: Runs 40, 55, 35, 60, 70 → sum 260 → average = 52.
- For consecutive numbers (like 11 to 19), average = (first + last)/2 = 15.
8. Time and work (काळ – काम)
- If A finishes a work in a days, A does 1/a of it in one day.
- A (a days) and B (b days) together: days = a × b / (a + b).
- Example: A in 10 days, B in 15 days → together 10 × 15 / 25 = 6 days.
9. Speed, time and distance (वेग – वेळ – अंतर)
- Distance = Speed × Time. To change km/h into m/s, multiply by 5/18; m/s into km/h, multiply by 18/5.
- Train passing a pole: distance = length of the train. Train passing a platform: distance = train + platform.
- Example: A 150 m train at 54 km/h (= 15 m/s) passes a 300 m platform in (150 + 300)/15 = 30 seconds.
10. Area and perimeter (क्षेत्रफळ – परिमिती)
| Shape | Area | Perimeter |
|---|---|---|
| Square (side a) | a² | 4a |
| Rectangle (l, b) | l × b | 2(l + b) |
| Triangle | ½ × base × height | sum of the 3 sides |
| Circle (radius r) | πr² | 2πr (circumference) |
- Use π = 22/7. Example: circle of radius 7 cm → area = 22/7 × 7 × 7 = 154 cm², circumference = 2 × 22/7 × 7 = 44 cm.
11. Ages and number tricks (वयवारी)
- Write today's ages with one letter. Example: the father is 3 times as old as the son; after 10 years he will be 2 times as old. Today: son = x, father = 3x → 3x + 10 = 2(x + 10) → x = 10. Son 10, father 30.
- Squares to remember: 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225, 16² = 256, 17² = 289, 18² = 324, 19² = 361, 25² = 625.
Practice MCQs (with answers)
Q1. What is 25% of 480?
- (A) 100
- (B) 120
- (C) 140
- (D) 96
Answer: (B) 120 – 480 × ¼ = 120.
Q2. An article bought for ₹800 is sold for ₹920. What is the profit percent?
- (A) 12%
- (B) 18%
- (C) 15%
- (D) 20%
Answer: (C) 15% – profit ₹120; 120/800 × 100 = 15.
Q3. Simple interest on ₹5,000 at 8% per year for 3 years?
- (A) ₹1,200
- (B) ₹1,000
- (C) ₹1,500
- (D) ₹1,800
Answer: (A) ₹1,200 – 5,000 × 8 × 3/100.
Q4. The average of 12, 15, 18, 21 and 24 is:
- (A) 17
- (B) 19
- (C) 20
- (D) 18
Answer: (D) 18 – sum 90 ÷ 5.
Q5. A can finish a work in 12 days and B in 6 days. Together they finish it in:
- (A) 3 days
- (B) 6 days
- (C) 4 days
- (D) 9 days
Answer: (C) 4 days – 12 × 6 / 18 = 4.
Q6. 54 km/h is how many metres per second?
- (A) 12
- (B) 18
- (C) 20
- (D) 15
Answer: (D) 15 – 54 × 5/18 = 15.
Q7. LCM of 12 and 18 is:
- (A) 6
- (B) 36
- (C) 72
- (D) 216
Answer: (B) 36.
Q8. ₹1,200 is divided in the ratio 3 : 5. The bigger share is:
- (A) ₹450
- (B) ₹600
- (C) ₹750
- (D) ₹800
Answer: (C) ₹750 – 1,200 × 5/8.
Q9. Compound interest on ₹10,000 at 10% per year for 2 years?
- (A) ₹2,100
- (B) ₹2,000
- (C) ₹2,200
- (D) ₹1,100
Answer: (A) ₹2,100 – amount 10,000 × 1.1 × 1.1 = 12,100.
Q10. A 200 m long train running at 72 km/h passes an electric pole in:
- (A) 20 seconds
- (B) 10 seconds
- (C) 15 seconds
- (D) 12 seconds
Answer: (B) 10 seconds – 72 km/h = 20 m/s; 200 ÷ 20 = 10.
Exam tip
Don't do long working for easy questions: use the shortcuts (½, ¼, 1/8 for 50%, 25%, 12.5%; × 5/18 for speed). If a question takes more than a minute, mark it and come back at the end.