Section C of Paper II has 6 questions × 5 marks of general arithmetic. Write every step: marks are given for method, not only the answer. Percentage and ratio have full notes in Percentage and Ratio and Proportion.
1. BODMAS (order of operations)
Brackets → Of → Division → Multiplication → Addition → Subtraction. Division and multiplication are done left to right; so are addition and subtraction.
- 18 ÷ 3 × 2 + 4 − 1 = 6 × 2 + 4 − 1 = 12 + 4 − 1 = 15
- 7 + 3 × (10 − 4) ÷ 2 = 7 + 3 × 6 ÷ 2 = 7 + 9 = 16
2. Unitary method (ऐकिक नियम)
Find the value of one unit first, then of the required number of units.
- Direct variation (more items → more cost): 5 pens cost Rs 75. 1 pen = 75 ÷ 5 = Rs 15. 8 pens = 15 × 8 = Rs 120.
- Inverse variation (more workers → fewer days): 6 men finish a job in 10 days. 1 man takes 6 × 10 = 60 days. 15 men take 60 ÷ 15 = 4 days.
- A car runs 240 km on 16 litres. 1 litre → 15 km. For 360 km: 360 ÷ 15 = 24 litres.
3. Fractions
| Operation | Rule | Example |
|---|---|---|
| Add/subtract | Make the denominators equal (LCM) | 2/3 + 1/4 = 8/12 + 3/12 = 11/12 |
| Multiply | Numerator × numerator, denominator × denominator | 3/4 × 2/5 = 6/20 = 3/10 |
| Divide | Multiply by the reciprocal | 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 |
| Compare | Convert to decimals or equal denominators | 5/8 = 0.625 > 3/5 = 0.6 |
4. Decimals
- 0.5 = 1/2, 0.25 = 1/4, 0.125 = 1/8, 0.2 = 1/5, 0.75 = 3/4.
- Multiply decimals as whole numbers, then count decimal places: 2.5 × 0.4 = 25 × 4 = 100 → two places → 1.00.
- Fraction to percentage: multiply by 100. 3/5 = 0.6 = 60%.
5. Percentage and ratio quick rules
- x% of y = x × y ÷ 100. 15% of 600 = 90.
- Divide Rs 1,200 in the ratio 2 : 3. Total parts 5. Shares: 1200 × 2/5 = 480 and 1200 × 3/5 = 720.
6. More solved examples
| Problem | Working | Answer |
|---|---|---|
| 18 − 6 ÷ 3 × 2 + 4 | Division and multiplication first: 6 ÷ 3 = 2, 2 × 2 = 4; then 18 − 4 + 4 | 18 |
| (5 + 3) × 2² − 10 | Brackets 8, power 4, multiply 32, subtract 10 | 22 |
| If 6 pens cost Rs 90, what do 10 pens cost? | One pen = 90 ÷ 6 = 15; 10 pens = 150 | Rs 150 |
| 8 workers finish a job in 15 days. How long for 12 workers? | Work = 8 × 15 = 120 worker-days; 120 ÷ 12 | 10 days |
| 3/4 + 2/3 | LCM 12: 9/12 + 8/12 = 17/12 | 1 5/12 |
| 0.25 × 0.4 | 25 × 4 = 100; four decimal places in total | 0.1 |
| Convert 3/8 to a percentage | 3 ÷ 8 = 0.375 × 100 | 37.5% |
7. Common errors
- Doing addition before multiplication: always follow BODMAS.
- In inverse proportion (more workers, fewer days) multiplying instead of dividing.
- Adding fractions by adding tops and bottoms (1/2 + 1/3 is not 2/5).
- Losing decimal places when multiplying decimals.
8. How this topic is asked in the exam
Kharidar and Nayab Subba papers include several short arithmetic items: one BODMAS simplification, one or two unitary method problems on cost, work or time, and fraction or decimal conversions. These are quick marks if you write each step. Check the answer by putting it back into the question.
📌 Key points to remember
- BODMAS: Brackets, Of, Division, Multiplication, Addition, Subtraction.
- Unitary method: find one unit first.
- Direct: multiply; inverse (work, days): multiply then divide.
- Fractions: LCM for add/subtract; multiply by reciprocal to divide.
- x% of y = xy/100; ratio share = total × part ÷ sum of parts.
Test yourself: Fundamental Operations, BODMAS, Unitary Method, Fractions and Decimals
50 questions check what you read about BODMAS (order of operations), Fractions and Percentage and ratio quick rules. Each attempt picks 25 at random.