In this guide
This is the sheet to read in the ten minutes before a mock and in the last week before the exam. It is not a place to learn a topic for the first time; each block links back to a full guide. What it adds is a one-line reason next to the formulas that people most often misremember. If you know why a formula works, you can rebuild it in the exam hall when memory fails.
Use it actively. Cover the right-hand column of each table and say the rule aloud before you look.
Fractions and percentages
| Fraction | Percent | Fraction | Percent |
|---|---|---|---|
| 1/3 | 33.33% | 1/9 | 11.11% |
| 1/6 | 16.67% | 1/11 | 9.09% |
| 1/7 | 14.29% | 1/12 | 8.33% |
| 1/8 | 12.5% | 1/15 | 6.67% |
| 3/8 | 37.5% | 1/16 | 6.25% |
| 5/8 | 62.5% | 7/8 | 87.5% |
| Rule | Formula | Why |
|---|---|---|
| Percentage change | (new − old) ÷ old × 100 | Change is measured against where you started |
| Successive changes a% and b% | a + b + ab/100 | The second change acts on the first change too |
| A is r% more than B | B is r ÷ (100 + r) × 100% less than A | The base switches from B to A |
| Price up r%, same spending | Consumption must fall by r ÷ (100 + r) × 100% | Same logic as the line above |
| Percentage points | A plain difference of two percentages | 20% to 25% is 5 points but a 25% rise |
Profit, loss and discount
| Rule | Formula | Why |
|---|---|---|
| Profit % and loss % | On cost price | Profit is judged against what you paid |
| Discount % | On marked price | The discount is taken off the label |
| Mark-up m%, discount d% | SP = CP × (1 + m/100) × (1 − d/100) | Two successive changes |
| Same SP, profit x% on one and loss x% on the other | Net loss of x²/100 % | The loss is on a bigger cost price |
| Buy x, get y free | Discount = y ÷ (x + y) | You pay for x out of x + y items |
Full guide: profit, loss and discount.
Interest
- SI = P × R × T ÷ 100. CI amount = P × (1 + R/100)ᵀ.
- CI − SI for 2 years = P × (R/100)². For 3 years = P × (R/100)² × (3 + R/100).
- Half-yearly: halve the rate, double the periods. Quarterly: rate ÷ 4, periods × 4.
- Under CI, if a sum doubles in n years, it becomes 4 times in 2n and 8 times in 3n.
- 10% multipliers: 1.1, 1.21, 1.331, 1.4641.
Full guide: simple and compound interest.
Ratio, averages, partnership and mixtures
| Rule | Formula | Why |
|---|---|---|
| Joining ratios | A : B = 2 : 3 and B : C = 4 : 5 give 8 : 12 : 15 | Make B the same in both (12) |
| Average | Sum ÷ count | Change the sum, then divide again |
| Partnership | Profit ratio = capital × time | Money working for longer earns more |
| Alligation | Cheaper : dearer = (dearer − mean) : (mean − cheaper) | Each side balances the other's distance from the mean |
| Repeated replacement | Pure left = V × (1 − x/V)ⁿ | Each round keeps the same fraction |
Time, work and speed
- Work: take total work as the LCM of the days; rates add, days do not.
- Adding three pair-rates counts each person twice.
- Person-hours are fixed: M₁ × D₁ × H₁ = M₂ × D₂ × H₂ for the same job.
- km/h × 5/18 = m/s, because 1,000 m ÷ 3,600 s = 5/18.
- Two equal distances at a and b: average speed = 2ab ÷ (a + b).
- Same direction subtract speeds; opposite directions add.
- Train passing a pole: its own length. Passing a platform or another train: the sum of lengths.
- Boat = (down + up) ÷ 2; stream = (down − up) ÷ 2.
Full guide: time, work, speed and distance.
Mensuration
| Shape | Area or volume | Surface |
|---|---|---|
| Circle | πr² | Circumference 2πr |
| Triangle | ½ × base × height | |
| Cylinder | πr²h | Curved 2πrh |
| Cone | ⅓πr²h | Curved πrl, where l is the slant height |
| Sphere | (4/3)πr³ | 4πr² |
| Hemisphere | (2/3)πr³ | Total 3πr² |
Use π = 22/7 when the radius is a multiple of 7.
P&C and probability
- Arrange: nPr. Choose: nCr = nPr ÷ r!.
- Repeated items: n! ÷ (p! × q!). Circle: (n − 1)!.
- "Together": treat as one block. "Never together": total minus together.
- P(not A) = 1 − P(A). Independent events multiply.
- Two dice: 36 outcomes. A pack: 52 cards, 12 face cards, 4 of each rank.
Full guide: probability and P&C.
DI habits
- Read the headings, units and footnotes before the first question.
- Weight averages by group size; never average percentages of different bases.
- "Which is highest?" questions need an order, not values. Compare fractions by cross-multiplying.
- Divide by the old value for a percentage change.
- Check whether an answer is asked in lakh, thousand or crore.
- If a set is slow after two questions, move on and come back.
See calculation shortcuts for speed methods.
Self-test: 16 questions in 12 minutes
- Write 3/8 as a percentage.
- Price rises 25%. By what percentage must consumption fall to keep spending the same?
- Cost ₹800, marked 25% above cost, sold at 10% discount. Profit %?
- SI on ₹5,000 at 6% a year for 3 years?
- CI on ₹10,000 at 10% a year for 2 years?
- A takes 10 days, B 15 days. Together?
- 72 km/h in m/s?
- A 240 m train passes a pole in 12 seconds. Speed in km/h?
- Rice at ₹40 and ₹55 a kg is mixed to cost ₹45 a kg. In what ratio?
- A invests ₹6,000 for 12 months and B ₹8,000 for 6 months. Profit ratio?
- The average of 6 numbers is 45. One is removed and the average becomes 42. What was removed?
- 7C2?
- Two dice are thrown. Probability that the sum is 7?
- Area of a circle of radius 14 cm?
- Volume of a cylinder with radius 7 cm and height 10 cm?
- A : B = 2 : 3 and B : C = 4 : 5. Find A : B : C.
Answers:
- 37.5%.
- 20%. 25 ÷ 125.
- 12.5%. SP = 800 × 1.25 × 0.9 = 900.
- ₹900. 5,000 × 6 × 3 ÷ 100.
- ₹2,100. 10,000 × 0.21.
- 6 days. 30 units; 3 + 2 a day.
- 20 m/s. 72 × 5/18.
- 72 km/h. 240 ÷ 12 = 20 m/s.
- 2 : 1 (₹40 rice to ₹55 rice). (55 − 45) : (45 − 40) = 10 : 5.
- 3 : 2. 72,000 : 48,000.
- 60. 6 × 45 − 5 × 42 = 270 − 210.
- 21. (7 × 6) ÷ 2.
- 1/6. Six outcomes out of 36.
- 616 cm². 22/7 × 196.
- 1,540 cm³. 22/7 × 49 × 10.
- 8 : 12 : 15.
If you get fewer than 13 right, go back to the full guide for each miss before your next mock.
Last-week checklist
- Read this sheet once a day, covering the "Why" column.
- One DI set of each type every day: table, bar or line, pie, caselet, missing data.
- Ten simplification or approximation questions a day.
- Redo the self-test on day 7; aim for 16 out of 16.
- Go through your DI error log for repeated traps, and follow the quant plan for the order of topics.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the State Bank of India website .
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