Remainder when 84 is divided by 3 is
Answer / solution
Correct option: C
84 = 3×28 + 0.
School boards · SSC · Railway · Banking
Mathematics practice for school and competitive exams
Use this hub to move from a formula, to one worked example, to a timed paper. Board students stay on the CBSE class tree. Competitive students open a chapter below and then a mock on the test-series path.
Formula map Shortcuts Start: Percentage CBSE Class 10 150 questions
How to study from this section
Do not read every chapter in one sitting. Pick the chapter your last mock marked wrong. Read the formula aloud, copy the worked example on paper, then sit a 20-minute subject mock. That loop is the product: study → practise → test → score → return.
CBSE Class 9–12 chapter questions (100 per chapter) remain at /cbse/. This /maths/ tree is the competitive + formula overlay so “maths formulas” and “percentage questions” have a clean URL that is not a copy of a class page.
Preparation order that actually works
- Percentage and ratio — they unlock profit-loss, mixture and DI.
- Average, ages, LCM/HCF — short chapters, frequent in GD and MTS.
- Time-work and TSD — same rate idea, different story.
- SI then CI — do not skip the conversion-period trap.
- Algebra and mensuration — CGL and board overlap.
- Trigonometry and probability — after the arithmetic base is stable.
If a mock shows you below 50% on a chapter, open that topic page, write the example by hand, then sit the same subject mock again. Repeating a full mixed paper without fixing the chapter wastes the attempt counter.
Chapter list
🔢 Number System
SSC GD, MTS, Railway, Police
Divisibility, remainders, LCM/HCF and place-value questions that decide easy marks.
➗ Simplification
SSC CHSL, MTS, Banking prelims
BODMAS, fractions and decimal cleanup — speed matters more than new theory.
% Percentage
Every SSC and banking paper
The base chapter for profit-loss, interest and data interpretation.
💹 Profit and Loss
SSC CGL, CHSL, GD, Railway
Cost price, marked price and successive discounts — one formula family.
⚖️ Ratio and Proportion
SSC, Railway, Police
Partnership, mixture and map-scale questions sit on this chapter.
📊 Average
SSC GD, MTS, Banking
Weighted means and “new average after joining/leaving” problems.
🛠️ Time and Work
SSC CGL, CHSL, Railway
One-day work, efficiency and combined work — keep units consistent.
🚰 Pipes and Cisterns
SSC CGL, CHSL
Inlet/outlet work with opposite signs. Same engine as time and work.
🚌 Time, Speed and Distance
SSC, Railway, Police
Unit conversion first, then average speed and relative speed.
🛶 Boats and Streams
SSC CGL, CHSL
Downstream = u+v, upstream = u−v. Do not swap still-water and current.
🏦 Simple Interest
SSC GD, MTS, Police
SI = PRT/100. Used as the baseline before compound interest.
📈 Compound Interest
SSC CGL, Banking
Amount = P(1+R/100)^n. Half-yearly and quarterly rates need a converted R and n.
🤝 Partnership
SSC CGL, CHSL
Profit share follows capital × time. Missing months change the ratio.
𝑥 Algebra
SSC CGL Tier-I/II, CBSE 9–10
Identities, linear equations and quadratic roots — board plus competitive.
△ Geometry
SSC CGL, CBSE 9–10
Triangles, circles and angle chasing. Draw the figure before you calculate.
📦 Mensuration
SSC, Railway, CBSE
2D then 3D. Keep π = 22/7 or 3.14 consistent inside one question.
∠ Trigonometry
SSC CGL, CBSE 10
Identities and heights-and-distances. Memorise the standard angles first.
📉 Statistics
CBSE 10, SSC CGL
Mean, median, mode and graphs. Board papers ask interpretation, not only formulas.
🎲 Probability
SSC CGL, CBSE 10
Favourable ÷ total. Cards, coins and dice — list the sample space.
🔀 Permutation and Combination
SSC CGL Tier-II, Banking
Order matters for nPr, not for nCr. Read “together / not together” twice.
📑 Data Interpretation
SSC CGL, Banking, Railway
Tables and bar graphs. Approximate first, then exact only if options are close.
🧪 Mixture and Alligation
SSC CGL, Banking
Alligation cross for two-price mixes. Check whether the mean is weighted.
🎂 Ages
SSC GD, MTS, Police
Present, past and future ages. One linear equation is usually enough.
🔗 LCM and HCF
SSC GD, MTS, Railway
HCF × LCM = product of two numbers. Word problems hide this identity.
Related
Physics formulas Chemistry formulas Test series All timed papers Repeated concepts
150 important maths practice questions
Original arithmetic practice for this page. Not labelled as previous-year SSC/railway items. Tap an option to mark it. Open “Answer” for the working.
Score: 0 / 0
(9 + 5) × 3 =
Answer / solution
Correct option: B
Add first: 14 × 3 = 42.
A number 480 is decreased by 15%. The new value is
Answer / solution
Correct option: C
New = 480×(100−15)/100 = 408.
MP = ₹240, discount = 25%. SP is
Answer / solution
Correct option: A
SP = MP×(100−d)/100 = 180.
Divide ₹180 in the ratio 6:7. The first part is
Answer / solution
Correct option: C
First = 6/(13)×180 = 83.
Average of 6 numbers is 32. A new number 40 is added. New average is
Answer / solution
Correct option: C
New avg = (195+40)/7 = 33.
A can finish a work in 18 days, B in 22 days. Together they finish it in (nearest whole day)
Answer / solution
Correct option: D
1/A+1/B = (40)/(396); days ≈ 10.
Inlet fills in 10 h, outlet empties in 14 h. Both open, tank fills in
Answer / solution
Correct option: D
Net = 1/10−1/14 = 4/(140); time = 35 h.
Speed 36 km/h for 2 hours. Distance is
Answer / solution
Correct option: B
D = S×T = 72 km.
Still water 14 km/h, current 2 km/h. Downstream speed is
Answer / solution
Correct option: B
u+v = 16.
Amount on ₹2000 at 25% SI for 4 years is
Answer / solution
Correct option: C
Amount = P+SI = 4000.
Amount on ₹2000 at 5% CI for 2 years is
Answer / solution
Correct option: B
P(1+R/100)² = 2205.
A invests 4 units for 8 months, B invests 3 units for 6 months. Profit ₹1800. A’s share is
Answer / solution
Correct option: D
Ratio = capital×time = 32:18; A = 1152.
(8 − 3)² equals
Answer / solution
Correct option: B
a²−2ab+b² = 25.
Each interior angle of a square is
Answer / solution
Correct option: D
A square has four right angles.
Area of a circle radius 7 (π=22/7) is
Answer / solution
Correct option: D
πr² = 22/7×49 = 154.
The value of cos 60° is
Answer / solution
Correct option: A
Standard angle.
Range of 12 and 33 is
Answer / solution
Correct option: A
Largest − smallest.
A fair die is rolled. P(getting 1) is
Answer / solution
Correct option: A
One face out of 6.
P(8,3) equals
Answer / solution
Correct option: C
nPr = 336.
Sales A=20, B=46. How much more is B than A?
Answer / solution
Correct option: A
Difference = 26.
Alligation: cheaper 32, dearer 44, mean 38. Mix ratio (cheap:dear) is
Answer / solution
Correct option: A
Distances from mean are equal, so 1:1.
A is 24, B is 18. Sum of present ages is
Answer / solution
Correct option: C
24+18=42.
HCF of 12 and 18 is
Answer / solution
Correct option: D
HCF = 6.
Unit digit of 12 × 18 is
Answer / solution
Correct option: B
Product = 216; unit digit 6.
(9 + 5) × 2 =
Answer / solution
Correct option: A
Add first: 14 × 2 = 28.
A number 640 is decreased by 35%. The new value is
Answer / solution
Correct option: A
New = 640×(100−35)/100 = 416.
CP = ₹300, SP = ₹350. Profit % is
Answer / solution
Correct option: D
Profit% = (350−300)/300×100 = 16%.
Divide ₹180 in the ratio 5:6. The first part is
Answer / solution
Correct option: A
First = 5/(11)×180 = 81.
Average of 6 numbers is 40. A new number 40 is added. New average is
Answer / solution
Correct option: C
New avg = (243+40)/7 = 40.
A invests 3 units for 8 months, B invests 3 units for 6 months. Profit ₹1800. A’s share is
Answer / solution
Correct option: D
Ratio = capital×time = 24:18; A = 1028.
(8 + 3)² equals
Answer / solution
Correct option: C
a²+2ab+b² = 121.
Range of 9 and 30 is
Answer / solution
Correct option: D
Largest − smallest.
Sales A=36, B=46. How much more is B than A?
Answer / solution
Correct option: C
Difference = 10.
Alligation: cheaper 32, dearer 40, mean 36. Mix ratio (cheap:dear) is
Answer / solution
Correct option: A
Distances from mean are equal, so 1:1.
A is 32, B is 26. Sum of present ages is
Answer / solution
Correct option: B
32+26=58.
HCF of 15 and 25 is
Answer / solution
Correct option: B
HCF = 5.
63 mod 3 is
Answer / solution
Correct option: C
Remainder = 0.
(9 + 5) × 6 =
Answer / solution
Correct option: A
Add first: 14 × 6 = 84.
A number 400 is decreased by 5%. The new value is
Answer / solution
Correct option: A
New = 400×(100−5)/100 = 380.
CP = ₹140, loss = 25%. SP is
Answer / solution
Correct option: B
SP = CP×(100−L)/100 = 105.
Divide ₹180 in the ratio 4:5. The first part is
Answer / solution
Correct option: C
First = 4/(9)×180 = 80.
Average of 6 numbers is 28. A new number 40 is added. New average is
Answer / solution
Correct option: D
New avg = (171+40)/7 = 30.
A invests 2 units for 8 months, B invests 3 units for 6 months. Profit ₹1800. A’s share is
Answer / solution
Correct option: C
Ratio = capital×time = 16:18; A = 847.
If 2x + 4 = 18, then x =
Answer / solution
Correct option: D
2x = 14; x = 7.
Range of 6 and 27 is
Answer / solution
Correct option: C
Largest − smallest.
Sales A=52, B=46. How much more is B than A?
Answer / solution
Correct option: A
Difference = -6.
Alligation: cheaper 32, dearer 56, mean 44. Mix ratio (cheap:dear) is
Answer / solution
Correct option: A
Distances from mean are equal, so 1:1.
A is 20, B is 14. Sum of present ages is
Answer / solution
Correct option: C
20+14=34.
HCF of 6 and 9 is
Answer / solution
Correct option: C
HCF = 3.
The next even number after 39 is
Answer / solution
Correct option: B
Next even = 40.
(9 + 5) × 5 =
Answer / solution
Correct option: D
Add first: 14 × 5 = 70.
A number 560 is decreased by 25%. The new value is
Answer / solution
Correct option: B
New = 560×(100−25)/100 = 420.
CP = ₹300, profit = 25%. SP is
Answer / solution
Correct option: B
SP = CP×(100+P)/100 = 375.
Divide ₹180 in the ratio 3:4. The first part is
Answer / solution
Correct option: A
First = 3/(7)×180 = 77.
Average of 6 numbers is 36. A new number 40 is added. New average is
Answer / solution
Correct option: B
New avg = (219+40)/7 = 37.
A invests 6 units for 8 months, B invests 3 units for 6 months. Profit ₹1800. A’s share is
Answer / solution
Correct option: B
Ratio = capital×time = 48:18; A = 1309.
If x + 3 = 6, then x =
Answer / solution
Correct option: C
x = 6−3 = 3.
Sales A=28, B=46. How much more is B than A?
Answer / solution
Correct option: D
Difference = 18.
Alligation: cheaper 32, dearer 52, mean 42. Mix ratio (cheap:dear) is
Answer / solution
Correct option: A
Distances from mean are equal, so 1:1.
A is 28, B is 22. Sum of present ages is
Answer / solution
Correct option: D
28+22=50.
HCF of 9 and 12 is
Answer / solution
Correct option: C
HCF = 3.
26² equals
Answer / solution
Correct option: A
Square = 676.
(9 + 5) × 4 =
Answer / solution
Correct option: C
Add first: 14 × 4 = 56.
A number 720 is decreased by 45%. The new value is
Answer / solution
Correct option: D
New = 720×(100−45)/100 = 396.
Two successive discounts 10% and 10% equal a single discount of
Answer / solution
Correct option: D
d1+d2−d1d2/100 = 19%.
Divide ₹180 in the ratio 2:3. The first part is
Answer / solution
Correct option: B
First = 2/(5)×180 = 72.
Average of 6 numbers is 24. A new number 40 is added. New average is
Answer / solution
Correct option: B
New avg = (147+40)/7 = 26.
A invests 5 units for 8 months, B invests 3 units for 6 months. Profit ₹1800. A’s share is
Answer / solution
Correct option: C
Ratio = capital×time = 40:18; A = 1241.
8² − 3² equals
Answer / solution
Correct option: D
(a−b)(a+b) = 55.
Sales A=44, B=46. How much more is B than A?
Answer / solution
Correct option: C
Difference = 2.
Alligation: cheaper 32, dearer 48, mean 40. Mix ratio (cheap:dear) is
Answer / solution
Correct option: A
Distances from mean are equal, so 1:1.
A is 36, B is 30. Sum of present ages is
Answer / solution
Correct option: C
36+30=66.
HCF of 7 and 14 is
Answer / solution
Correct option: A
HCF = 7.
Remainder when 120 is divided by 3 is
Answer / solution
Correct option: B
120 = 3×40 + 0.
MP = ₹400, discount = 25%. SP is
Answer / solution
Correct option: C
SP = MP×(100−d)/100 = 300.
CP = ₹140, SP = ₹190. Profit % is
Answer / solution
Correct option: C
Profit% = (190−140)/140×100 = 35%.
CP = ₹300, loss = 25%. SP is
Answer / solution
Correct option: A
SP = CP×(100−L)/100 = 225.
If 2x + 4 = 20, then x =
Answer / solution
Correct option: A
2x = 16; x = 8.
CP = ₹140, profit = 25%. SP is
Answer / solution
Correct option: B
SP = CP×(100+P)/100 = 175.
Remainder when 156 is divided by 3 is
Answer / solution
Correct option: C
156 = 3×52 + 0.
FAQs
Are these previous-year SSC questions?
No year or shift is claimed on these pages. Each maths section has 150 original practice MCQs. When a verified source database exists, a question will show exam + year; until then it is practice.
Where are Class 10 board formulas?
The CBSE formula sheet at /cbse/class-10/mathematics/formulas/ stays the canonical board list. This maths hub links to it instead of copying every line.
Do you publish tricks that are only sometimes true?
Every shortcut page states when the trick must not be used. A speed trick that fails on close options is not published as if it were a theorem.
