Arithmetic — Speed Techniques for the Prelims Paper
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Chapter 21: Arithmetic — Speed Techniques for the Prelims Paper
Paper 1 of the AP SI and Constable Prelims gives you roughly 100 questions to answer inside three hours, and arithmetic typically accounts for twenty to twenty-five of those marks. On paper that sounds generous. In practice, most candidates burn eight to ten minutes on a single interest or percentage question because they solve it the way a textbook taught them — full formula, full expansion, full long division. A candidate who has internalised the shortcuts in this chapter can dispatch the same question in ninety seconds, and that saved time compounds across the paper. Over a hundred questions, a two-minute-per-question average versus a ninety-second average is the difference between finishing with time to review and rushing the last fifteen questions blind. Speed arithmetic is not a party trick; it is the single highest-leverage skill you can build for this exam, because unlike static GK it rewards practice with a predictable, near-linear improvement curve. Every technique below is built for pen-free or minimal-scratch-work calculation, because in the actual exam hall you will have an OMR sheet, a question booklet, and very little space to work in the margins.
1. Number System Shortcuts You Must Automate
Before percentages and interest, get the raw number sense right. Three habits pay for themselves across the whole paper.
Squares of numbers close to a round base. To square any number near a multiple of 10, use (a+b)² = a² + 2ab + b². For 47², treat it as (50-3)²: 50² - 2×50×3 + 3² = 2500 - 300 + 9 = 2209. For 63², treat it as (60+3)²: 3600 + 360 + 9 = 3969. This is far faster than long multiplication and it is the backbone of quick square-root estimation for DI questions too.
Multiplication by 5, 25, 125, and 15. Multiplying by 5 is the same as multiplying by 10 and halving: 84 × 5 = 840 ÷ 2 = 420. Multiplying by 25 is multiplying by 100 and dividing by 4: 88 × 25 = 8800 ÷ 4 = 2200. Multiplying by 125 is multiplying by 1000 and dividing by 8: 96 × 125 = 96000 ÷ 8 = 12000. Multiplying by 15 is ×10 plus half of that: 62 × 15 = 620 + 310 = 930. None of these need a written multiplication table lookup — they turn multiplication into halving and doubling, which the brain does much faster.
Digit-sum divisibility for elimination. In "which of the following is divisible by 9" type questions, add the digits. 4536 → 4+5+3+6 = 18, divisible by 9, so 4536 is too. This single check eliminates two of four options in under five seconds, turning a calculation question into an elimination question.
2. Percentage-to-Fraction Conversion — The Single Biggest Time-Saver
Every percentage has an exact fraction equivalent, and multiplying by a simple fraction is almost always faster than multiplying by a decimal. Memorise this table cold — not "know roughly," but recall instantly, the way you recall your own date of birth.
| Percentage | Fraction | Percentage | Fraction |
| 50% | 1/2 | 16.66% | 1/6 |
| 33.33% | 1/3 | 14.28% | 1/7 |
| 25% | 1/4 | 12.5% | 1/8 |
| 20% | 1/5 | 11.11% | 1/9 |
| 10% | 1/10 | 9.09% | 1/11 |
| 75% | 3/4 | 8.33% | 1/12 |
| 66.66% | 2/3 | 6.25% | 1/16 |
| 37.5% | 3/8 | 4% | 1/25 |
| 62.5% | 5/8 | 5% | 1/20 |
Worked example — slow method versus fast method. Find 37.5% of 640.
Slow method: 37.5% of 640 = 640 × 0.375. You would multiply 640 × 375 = 240000, then place the decimal three places back = 240. This needs a full multi-digit multiplication.
Fast method: 37.5% = 3/8. So 640 × 3/8 = (640 ÷ 8) × 3 = 80 × 3 = 240. Same answer, but you divided by 8 (easy, since 640 is a familiar multiple) and multiplied by 3 (trivial). Total mental steps: two, both single-digit-friendly.
Worked example 2. Find 12.5% of 480.
Fast method: 12.5% = 1/8. 480 ÷ 8 = 60. Done in one step. The slow decimal method (480 × 0.125) requires you to multiply 480 by 125 and shift the decimal — three times the mental load for the same answer.
Worked example 3 — successive percentage change. A candidate's marks increased by 20% in the second attempt, then decreased by 10% in the third attempt compared to the second. What is the net percentage change from the first attempt?
Slow method: Assume marks = 100. After +20%: 120. After -10% of 120: 120 - 12 = 108. Net change = +8%.
Fast method using the successive-percentage formula: Net% = a + b + ab/100, where a = +20 and b = -10. Net% = 20 - 10 + (20 × -10)/100 = 10 - 2 = 8%. This formula lets you combine any two (or, applied twice, any number of) successive percentage changes in one line without picking a base value at all — useful when the question gives you the percentages directly and asks only for the combined effect.
3. Simple Interest and Compound Interest — Approximation That Beats the Formula
SI and CI questions are the most formula-heavy part of prelims arithmetic, and also the most shortcut-friendly, because the compound interest formula P(1+R/100)^T is genuinely painful to compute by hand for T = 2 or 3 years, yet a close approximation gets you to the exact answer almost every time when the numbers are exam-friendly.
Simple Interest — direct fraction method. SI = PRT/100. For P = 8000, R = 10%, T = 3 years: SI = 8000 × 10 × 3 / 100 = 8000 × 30/100 = 8000 × 0.3 = 2400. Faster: 10% of 8000 is 800 (shift decimal), and SI for 3 years at simple rate is just 3 × (one year's interest) = 3 × 800 = 2400. Once you have one year's interest, SI for any number of years is pure multiplication — no need to re-run the formula.
Compound Interest — the additive shortcut for 2 years. For 2 years, effective CI% = 2R + R²/100. At R = 10%: effective% = 20 + 100/100 = 21%. Check against the exact formula: 8000 × 0.21 = 1680; using compound formula, 8000 × 1.21 = 9680, CI = 1680. Matches exactly, because (1+R/100)² - 1 = 2R/100 + (R/100)², which is precisely 2R% + R²/100% when expressed as a percentage. This is not an approximation for round numbers — it is algebraically exact.
Compound Interest — the additive shortcut for 3 years. Effective% = 3R + 3R²/100 + R³/10000. At R = 10%: 30 + 3(100)/100 + 1000/10000 = 30 + 3 + 0.1 = 33.1%. On P = 8000: CI = 8000 × 0.331 = 2648. Verify against the direct formula: 8000 × 1.10³ = 8000 × 1.331 = 10648, so CI = 2648. Exact match. The 3-year formula looks intimidating the first time you see it, but once memorised it converts a cube calculation into three small additions.
Worked example — difference between CI and SI for 2 years (a very common question type). Find the difference between CI and SI on Rs 15,000 at 8% for 2 years.
Key shortcut: For 2 years, CI - SI = P × (R/100)². This is because the only term CI has that SI doesn't, at 2 years, is the "interest on interest" term, which is exactly P(R/100)². Here: 15000 × (8/100)² = 15000 × 0.0064 = 96. You never need to compute CI and SI separately and subtract — one multiplication gives the answer directly. This shortcut alone resolves an entire sub-category of Prelims questions in under twenty seconds.
4. Ratio and Proportion Shortcuts
Ratio questions dominate the "divide in a given ratio," "compare efficiencies," and "mixture and alligation" sub-types. The core habit is to stop converting ratios to actual values until the very last step.
Worked example — dividing an amount in a given ratio. Divide Rs 4,200 among A, B and C in the ratio 2:3:5.
Fast method: Total parts = 2+3+5 = 10. Value of one part = 4200/10 = 420. A = 2×420 = 840, B = 3×420 = 1260, C = 5×420 = 2100. Check: 840+1260+2100 = 4200. Correct. The entire calculation depends on making "value of one part" the pivot number — compute it once, then every share is a single multiplication.
Worked example — combining two ratios (a common trap question). If A:B = 3:4 and B:C = 5:7, find A:B:C.
Fast method: Make B's value common by taking the LCM of 4 and 5, which is 20. A:B = 3:4 = 15:20 (multiplied by 5). B:C = 5:7 = 20:28 (multiplied by 4). Now B matches at 20 in both. So A:B:C = 15:20:28. This LCM-bridge method avoids fractions entirely and is far faster than converting each ratio to a decimal.
Alligation shortcut for mixture questions. To mix two quantities at prices/rates C1 and C2 to get a mean rate Cm, the ratio of quantities is (C2 - Cm) : (Cm - C1) — cross-subtract, don't cross-multiply. Example: mix tea at Rs 40/kg and Rs 60/kg to get a mean of Rs 45/kg. Ratio = (60-45):(45-40) = 15:5 = 3:1. So for every 3 kg of the cheaper tea (Rs 40), you need 1 kg of the costlier tea (Rs 60). Verify: (3×40 + 1×60)/4 = (120+60)/4 = 180/4 = 45. Correct.
5. Speed, Distance and Time — Unit-Conversion Shortcuts
A huge fraction of time lost in this topic comes from clumsy unit conversion. Two facts eliminate that entirely.
km/h to m/s: multiply by 5/18. 45 km/h = 45 × 5/18 = 225/18 = 12.5 m/s. Do not convert km to m and hours to seconds separately — the 5/18 factor already encodes both conversions (1000/3600 simplifies to 5/18).
m/s to km/h: multiply by 18/5. 20 m/s = 20 × 18/5 = 360/5 = 72 km/h.
Worked example — trains crossing each other. Two trains of length 150 m and 100 m run in opposite directions at 54 km/h and 36 km/h. How long do they take to cross each other?
Fast method: In opposite directions, relative speed = sum of speeds = 54+36 = 90 km/h. Convert once: 90 × 5/18 = 25 m/s. Total distance to cover = sum of lengths = 150+100 = 250 m. Time = distance/speed = 250/25 = 10 seconds. Note that you convert speed to m/s only once, right before the final division — converting earlier and working with decimals throughout wastes time.
6. Averages — the Deviation Method
Rather than adding all values and dividing, pick a convenient assumed average and work with deviations, especially useful when numbers cluster near a round figure.
Worked example. Find the average of 78, 82, 91, 69, 85.
Fast method: Assume average = 80. Deviations: 78-80=-2, 82-80=+2, 91-80=+11, 69-80=-11, 85-80=+5. Sum of deviations = -2+2+11-11+5 = 5. Average = assumed average + (sum of deviations)/n = 80 + 5/5 = 80+1 = 81. Verify by direct addition: 78+82+91+69+85 = 405, 405/5 = 81. Matches. The deviation method turns a five-number addition of large values into an addition of small, mostly single-digit numbers — much less error-prone under time pressure.
7. Profit and Loss — the Single-Fraction Method
Profit and loss questions repeatedly ask you to find cost price from selling price and profit percentage, or vice versa. The textbook method sets up an equation with x as the unknown cost price; the fast method treats profit or loss percentage as a multiplying factor applied once.
Worked example. A shopkeeper sells an article for Rs 828 at a profit of 15%. Find the cost price.
Slow method: Let CP = x. SP = x + 15% of x = 1.15x. So 1.15x = 828, x = 828/1.15 = 720. This needs a division by a decimal, which is clumsy without a calculator.
Fast method: Convert 115% to a fraction over 100: SP/CP = 115/100 = 23/20. So CP = SP × 20/23 = 828 × 20/23. Since 828 = 23 × 36, this becomes 36 × 20 = 720. Recognising that the selling price is often a clean multiple of the percentage's fraction denominator is the real skill here — exam-setters build the numbers that way on purpose, so actively look for the factor before you start dividing.
Worked example — successive discounts. A shirt with marked price Rs 1,200 is sold after two successive discounts of 10% and 5%. Find the selling price.
Fast method: Apply the discounts as fractions in sequence. After 10% off: 1200 × 9/10 = 1080. After a further 5% off: 1080 × 19/20 = 1080 × 0.95 = 1026. Alternatively, use the successive-percentage formula for the combined discount: -10 + -5 + (-10×-5)/100 = -15 + 0.5 = -14.5%. Check: 1200 × 0.855 = 1026. Both routes match, but for two-discount problems the direct fraction chaining is usually the faster of the two because you avoid computing a combined percentage first.
8. Time and Work — The Efficiency Table Method
Time and work questions become mechanical the moment you stop working with "days" and start working with "work done per day," expressed as a fraction of the total job, or better, as units of work per day using LCM.
Worked example. A can complete a piece of work in 12 days, B in 15 days. Working together, how many days will they take?
Fast method: Take total work = LCM(12,15) = 60 units. A's rate = 60/12 = 5 units/day. B's rate = 60/15 = 4 units/day. Combined rate = 9 units/day. Time together = 60/9 = 20/3 = 6 and 2/3 days. This LCM-as-total-work trick converts every time-and-work question into whole-number arithmetic — no fractions of a day appear until the very last division, and often not even then.
Worked example — work and wages. A, B and C together earn Rs 1,800 for a job. A can do the job alone in 6 days, B in 8 days, and C in 12 days. Find C's share of the earnings.
Fast method: Total work = LCM(6,8,12) = 24 units. A's rate = 4/day, B's rate = 3/day, C's rate = 2/day. Wages are split in the ratio of work contributed, which equals the ratio of rates: 4:3:2, total 9 parts. C's share = 1800 × 2/9 = 400. Once again, the LCM conversion removes every fraction from the problem until the final ratio division.
9. Number Series and Simplification — the BODMAS Shortcut Habit
Simplification questions ("find the value of…") test whether you can execute BODMAS quickly and without slips, not whether you understand the rule — everyone does. Two habits save real time here.
Habit one: scan for cancellation before multiplying. For an expression like (15 × 24)/(9 × 40), do not multiply the numerator and denominator separately. Instead cancel: 15/9 × 24/40 = 5/3 × 3/5 = 1. Recognising common factors across the fraction bar before multiplying turns a two-step multiplication-then-division into instant cancellation.
Habit two: convert repeating decimals to fractions instantly. 0.333... = 1/3, 0.1666... = 1/6, 0.8333... = 5/6. When these show up inside a simplification expression, replacing them with fractions immediately avoids carrying long decimals through several operations.
Worked example. Simplify: 0.75 × 0.4 ÷ 0.15.
Fast method: Convert to fractions: 3/4 × 2/5 ÷ 3/20 = 3/4 × 2/5 × 20/3. Cancel the 3s: 1/4 × 2/5 × 20/1 = (2×20)/(4×5) = 40/20 = 2. This is far quicker and far less error-prone than multiplying decimals (0.75×0.4 = 0.3, then 0.3/0.15 = 2) once the numbers get uglier than this illustrative case — the fraction-cancellation habit scales to harder numbers where decimal multiplication does not.
10. Boats and Streams — the Sum-and-Difference Shortcut
This sub-topic is a direct extension of speed-distance-time, and it always reduces to the same pair of relationships: downstream speed = boat speed + stream speed, upstream speed = boat speed - stream speed. The shortcut is to never solve for boat speed and stream speed via simultaneous equations when you can instead read them straight off the sum and difference.
Worked example. A boat covers 24 km downstream in 2 hours and returns upstream in 3 hours. Find the speed of the boat in still water and the speed of the stream.
Fast method: Downstream speed = 24/2 = 12 km/h. Upstream speed = 24/3 = 8 km/h. Boat speed (still water) = average of the two = (12+8)/2 = 10 km/h. Stream speed = half the difference = (12-8)/2 = 2 km/h. No equation-solving required — sum halved gives boat speed, difference halved gives stream speed, directly from the definitions above.
11. Percentage Point Traps — Reading the Question Correctly
A meaningful share of marks lost in this section come not from calculation errors but from misreading what is actually being asked. Three traps recur across every mock paper on the platform.
Trap one: "increase by 20%" versus "increase to 20%." The first means multiply by 1.20; the second means the new value simply is 20. Exam-setters rely on candidates skimming past the preposition.
Trap two: percentage of what base. "Ravi's salary is 20% more than Suresh's" is not the same as "Suresh's salary is 20% less than Ravi's." If Suresh earns 100, Ravi earns 120. But going the other way, if Ravi earns 120, Suresh earns 120/1.20 = 100, which is indeed 20/120 = 16.67% less than Ravi, not 20% less. Always identify whose value is the base (the "of" in "x% of y") before writing any equation.
Trap three: percentage change versus percentage point change. If a pass percentage rises from 40% to 50%, that is a 10 percentage point increase, but a (50-40)/40 = 25% relative increase. Prelims questions sometimes ask for one, sometimes the other, in near-identical phrasing — read the exact words "percentage increase" versus "percentage point increase" before committing to an answer.
12. LCM and HCF — the Prime-Factor Ladder
Questions on "find the least number which when divided by 6, 8 and 12 leaves remainder 3 in each case" or "find the greatest number that divides 48 and 60 exactly" appear regularly, and the fast method is always the same ladder: break every number into prime factors, then pick either the highest or lowest power of each prime depending on whether you need LCM or HCF.
Worked example — LCM. Find the LCM of 18, 24 and 30.
Fast method: 18 = 2×3², 24 = 2³×3, 30 = 2×3×5. LCM takes the highest power of each prime present: 2³ × 3² × 5 = 8×9×5 = 360.
Worked example — HCF. Find the HCF of 48 and 60.
Fast method: 48 = 2⁴×3, 60 = 2²×3×5. HCF takes the lowest power of each common prime: 2² × 3 = 12.
Worked example — the "leaves remainder" variant. Find the least number which when divided by 6, 8 and 12 leaves remainder 3 in each case.
Fast method: First find LCM(6,8,12) = 24 (since 6=2×3, 8=2³, 12=2²×3, LCM = 2³×3 = 24). The required number is LCM + remainder = 24+3 = 27. Check: 27÷6 = 4 remainder 3; 27÷8 = 3 remainder 3; 27÷12 = 2 remainder 3. Correct in every case. The rule "LCM plus common remainder" replaces what would otherwise be trial and error.
13. Ages — the Present-and-Future Ratio Trick
Age problems are ratio problems in disguise, and the fast route treats the ratio as a single variable multiplier rather than setting up two separate unknowns.
Worked example. The present ages of A and B are in the ratio 3:5. After 6 years, the ratio of their ages will be 2:3. Find their present ages.
Fast method: Let present ages be 3x and 5x. After 6 years: (3x+6)/(5x+6) = 2/3. Cross-multiply: 3(3x+6) = 2(5x+6) → 9x+18 = 10x+12 → x = 6. Present ages: A = 18, B = 30. Check: after 6 years, A = 24, B = 36, ratio 24:36 = 2:3. Correct. The single variable x, tied directly to the given ratio, collapses what looks like a two-unknown problem into one linear equation.
14. Partnership — Profit Sharing by Capital-Time Product
Partnership questions where partners invest different amounts for different durations always resolve through one rule: profit share is proportional to the product of capital and time invested, not capital alone.
Worked example. A invests Rs 20,000 for the full year. B invests Rs 15,000 but joins after 4 months (so invests for 8 months). If the annual profit is Rs 9,300, find each partner's share.
Fast method: A's capital-time = 20,000×12 = 240,000. B's capital-time = 15,000×8 = 120,000. Simplify the ratio by dividing both by 60,000: 240,000:120,000 = 2:1. Total parts = 3. A's share = 9300 × 2/3 = 6200. B's share = 9300 × 1/3 = 3100. Check: 6200+3100 = 9300. Correct. Simplifying the capital-time ratio before applying it to the profit is what keeps the numbers small and the arithmetic fast.
15. Percentage Shortcuts for Population and Depreciation Problems
Population growth and machinery depreciation questions use the same compound-multiplication structure as compound interest, just applied to a quantity instead of money, and sometimes with a negative rate (depreciation).
Worked example. The population of a town is 40,000. It increases by 10% in the first year and decreases by 10% in the second year. Find the population after 2 years.
Fast method: Apply the successive-percentage formula: net% = 10 + (-10) + (10×-10)/100 = 0 - 1 = -1%. Population after 2 years = 40,000 × 0.99 = 39,600. Note that a +10% followed by a -10% does not cancel out to zero — this is one of the most commonly tested "gotcha" facts in the whole percentage chapter, and the successive-percentage formula makes the reason transparent: the second percentage is applied to a larger (or smaller) base than the first.
Worked example — depreciation. A machine worth Rs 50,000 depreciates at 10% per annum. Find its value after 2 years.
Fast method: Depreciation is compound reduction, so use the 2-year effective-percentage shortcut with a negative rate. Net% = 2(-10) + (-10)²/100 = -20 + 1 = -19%. Value after 2 years = 50,000 × 0.81 = 40,500. Direct check: 50,000 × 0.9 × 0.9 = 50,000 × 0.81 = 40,500. Matches, confirming the shortcut works identically for depreciation as it does for growth, provided you carry the sign through correctly.
16. Building Exam-Hall Speed: A Practical Drill Routine
Knowing a shortcut and executing it under exam pressure in fifteen seconds are different skills, and the gap between them closes only through timed repetition. Structure your last three weeks of arithmetic preparation around three drill types rather than more topic reading.
Drill one — the sixty-second percentage sprint. Write out ten random percentage-of-number questions (mix clean fractions like 25%, 37.5% with awkward ones like 17%, 23%) and give yourself sixty seconds for all ten. The goal is not perfection on day one; it is measuring your baseline and watching the completion count rise across a week of daily repetition.
Drill two — the formula-to-shortcut conversion drill. Take any five CI/SI questions from a previous mock and solve each one twice: once with the full formula, once with the shortcut from this chapter. Time both. This builds the trust needed to abandon the formula entirely on exam day, because you will have personally verified, dozens of times, that the shortcut gives an identical answer faster.
Drill three — the elimination-first pass. Before attempting full calculation on any arithmetic MCQ, spend three seconds checking whether the answer options let you eliminate two of the four outright — using digit-sum divisibility, rough magnitude estimation, or the "increase can't exceed X" logic. This single habit, applied across a hundred questions, saves several minutes in aggregate even though each individual save looks trivial.
None of these drills require new content. They require you to rehearse the techniques above until they stop feeling like techniques and start feeling like reflexes — the same way an experienced cashier makes change without consciously subtracting. That reflex-level fluency is exactly what separates a candidate who finishes Paper 1 with twenty minutes to review from one who is still calculating when the invigilator calls time.
Speed-Technique Checklist
- Convert every percentage in the question to its fraction form before doing any multiplication.
- For 2-year CI, use effective% = 2R + R²/100; for 3-year CI, use 3R + 3R²/100 + R³/10000.
- For "CI minus SI over 2 years" questions, jump straight to P(R/100)² — never compute CI and SI separately.
- For ratio division, always find the "value of one part" first, then multiply — never solve for each share independently.
- For two combined ratios, bridge on the common term using its LCM rather than converting to decimals.
- For alligation, cross-subtract (C2-Cm):(Cm-C1) — do not attempt to set up simultaneous equations.
- Memorise 5/18 (km/h to m/s) and 18/5 (m/s to km/h) as instant reflexes, not formulas to derive.
- Use the deviation method for averages whenever the numbers cluster near a round figure.
- Use digit-sum divisibility (by 3 and 9) to eliminate options before calculating exact values.
- Practice squaring numbers near multiples of 10 using (a±b)² until it takes under three seconds per number.
Practice MCQs
- Find 62.5% of 320.
- (a) 180
- (b) 190
- (c) 200
- (d) 210
- A trader marks up goods by 25% and then offers a 20% discount on the marked price. What is the net effect on the original price?
- (a) No change
- (b) 5% loss
- (c) 5% gain
- (d) 10% loss
- Find the compound interest on Rs 12,000 at 10% per annum for 2 years.
- (a) Rs 2,400
- (b) Rs 2,520
- (c) Rs 2,600
- (d) Rs 2,880
- Find the difference between CI and SI on Rs 20,000 at 5% for 2 years.
- (a) Rs 40
- (b) Rs 45
- (c) Rs 50
- (d) Rs 55
- Divide Rs 3,600 among A, B and C in the ratio 4:5:9. Find B's share.
- (a) Rs 900
- (b) Rs 1,000
- (c) Rs 1,100
- (d) Rs 1,200
- If A:B = 2:3 and B:C = 4:5, find A:B:C.
- (a) 8:12:15
- (b) 2:3:5
- (c) 4:6:9
- (d) 6:9:10
- In what ratio should tea at Rs 30/kg be mixed with tea at Rs 50/kg to get a mixture worth Rs 35/kg?
- (a) 1:3
- (b) 3:1
- (c) 2:3
- (d) 1:1
- Convert 72 km/h into m/s.
- (a) 15 m/s
- (b) 18 m/s
- (c) 20 m/s
- (d) 22 m/s
- Two trains, 120 m and 180 m long, run in the same direction at 72 km/h and 54 km/h. How long will the faster train take to cross the slower one?
- (a) 40 seconds
- (b) 50 seconds
- (c) 60 seconds
- (d) 70 seconds
- Find the average of 112, 108, 121, 95, 119.
- (a) 109
- (b) 110
- (c) 111
- (d) 113
- 47² equals:
- (a) 2179
- (b) 2189
- (c) 2199
- (d) 2209
- What is 11.11% of 900, expressed using the fraction shortcut?
- (a) 90
- (b) 99
- (c) 100
- (d) 110
- A sum becomes Rs 9,680 in 2 years at 10% per annum compound interest. Find the principal.
- (a) Rs 7,500
- (b) Rs 7,800
- (c) Rs 8,000
- (d) Rs 8,200
- Which of the following is divisible by 9: 4536, 4522, 4547, 4519?
- (a) 4522
- (b) 4536
- (c) 4547
- (d) 4519
- 96 × 125 using the shortcut equals:
- (a) 11,000
- (b) 11,500
- (c) 12,000
- (d) 12,500