Numerical Ability — DSSSB TGT Section A (20 marks)
Formulas + short methods. Keep a calculator-free speed habit (mental % and ratios).
1. Number System
| Item | Formula / fact |
|---|---|
| Divisibility 2 | Last digit even |
| 3 | Sum of digits ÷3 |
| 4 | Last 2 digits ÷4 |
| 5 | Ends 0 or 5 |
| 8 | Last 3 digits ÷8 |
| 9 | Sum of digits ÷9 |
| 11 | Alternating sum ÷11 |
| LCM × HCF | = product (two numbers) |
| Even / Odd | Even±Even=Even; Odd±Odd=Even; Even±Odd=Odd |
| Prime | >1, factors only 1 and itself |
Method: Factorise for LCM/HCF; remainder problems → write N = dq + r.
Example: HCF(12,18)=6; LCM=36; check 12×18=216=6×36.
2. Simplification (BODMAS)
Order: Brackets → Orders (powers/roots) → Division & Multiplication (L→R) → Addition & Subtraction (L→R).
Tips: Cancel factors early; convert mixed fractions; for of, treat as multiplication.
Example: 15 − 8 ÷ 2 × 3 = 15 − 4 × 3 = 15 − 12 = 3 (not (15−8)÷…).
3. Ratio & Proportion
| Concept | Formula |
|---|---|
| Ratio a:b | a/b |
| Proportion a:b = c:d | ad = bc |
| Divide N in a:b | Parts: a/(a+b)×N , b/(a+b)×N |
| a:b and b:c | a🅱️c = a×b : b×b : b×c (align middle) or cross-scale |
Example: Divide 80 in 3:5 → 30 and 50.
4. Percentage
| Concept | Formula |
|---|---|
| x% of N | (x/100)×N |
| A is what % of B | (A/B)×100 |
| % change | ((New−Old)/Old)×100 |
| Successive % | Net = a + b + ab/100 (a,b with signs) |
| x% ↑ then x% ↓ | Net loss = (x²/100)% |
Example: 20% of 250 = 50. Successive +10% then −10% on 100 → 99 (net −1%).
5. Average
| Concept | Formula |
|---|---|
| Average | Sum / n |
| Weighted avg | (w₁x₁ + w₂x₂)/(w₁+w₂) |
| Avg of first n naturals | (n+1)/2 |
Method: Deviation method — assume mean, adjust.
Example: Avg of 10, 20, 30 = 20.
6. Profit & Loss
| Concept | Formula |
|---|---|
| Profit | SP − CP (if SP>CP) |
| Loss | CP − SP |
| Profit % | (Profit/CP)×100 |
| Loss % | (Loss/CP)×100 |
| SP | CP × (100+P%)/100 |
| CP | SP × 100/(100+P%) |
| Discount | MP − SP; Disc% on MP |
Trap: Profit% always on CP unless said otherwise; discount on MP.
Example: CP=200, Profit 10% → SP=220.
7. Simple Interest & Compound Interest
| Concept | Formula |
|---|---|
| SI | (P×R×T)/100 |
| Amount (SI) | P + SI |
| CI (annual) | A = P(1+R/100)^T |
| CI | A − P |
| Diff CI−SI (2 yrs) | P(R/100)² |
| CI half-yearly | Rate R/2, time 2T periods |
Example: P=1000, R=10%, T=2; SI=200; CI=210; Diff=10.
8. Time & Work
| Concept | Formula |
|---|---|
| Work rate | 1/T per day (if finishes in T days) |
| A+B together | 1/A + 1/B |
| Man-days | M₁D₁ = M₂D₂ (same work) |
| Efficiency ∝ | 1/time |
Example: A=10 days, B=15 days → together 1/10+1/15=1/6 → 6 days.
9. Time–Speed–Distance
| Concept | Formula |
|---|---|
| Distance | Speed × Time |
| Avg speed (equal dist) | 2xy/(x+y) |
| Avg speed (equal time) | (x+y)/2 |
| km/h ↔ m/s | ×5/18 or ×18/5 |
| Relative (same dir) | |u−v| |
| Relative (opposite) | u+v |
| Train length | Speed × time to pass pole |
| Pass platform | (Train+Platform)/Speed = time |
Example: 72 km/h = 72×5/18 = 20 m/s.
10. Data Interpretation — Tips
- Read title, units, footnotes first (%, thousand, lakh).
- Approximate when options are far apart.
- For pie: 360° = total; angle/360 × total = value.
- For tables: compute only asked rows/columns.
- % of total vs % change — don’t mix.
- Check if stacked bar needs sum of segments.
- Ratio questions: cancel common factors before multiplying.
- If calculation heavy, eliminate options (parity, magnitude).
Formula tables (quick revision)
Core arithmetic
| Topic | Key formula |
|---|---|
| % | (part/whole)×100 |
| Ratio divide | a/(a+b)×N |
| Average | Σx / n |
| P&L | SP = CP(100±P%)/100 |
| SI | PRT/100 |
| CI | P(1+R/100)^n − P |
| Work | 1/A + 1/B = 1/T |
| Speed | D = S×T |
| Harmonic avg speed | 2xy/(x+y) |
Conversion & misc
| Convert | Rule |
|---|---|
| km/h → m/s | ×5/18 |
| m/s → km/h | ×18/5 |
| Successive % | a+b+ab/100 |
| CI−SI (2 yr) | PR²/100² |
Exam habit: Attempt easy BODMAS/%/ratio first; leave lengthy DI for last within the 20.