Remainder when 84 is divided by 3 is
Answer / solution
Correct option: C
84 = 3×28 + 0.
Speed with a warning label
Mathematics shortcut tricks (with limits)
A shortcut is allowed only when it is algebraically the same as the long method, or when the options are far enough that a controlled approximation cannot pick the wrong choice.
1. Successive percentage change
Problem type. A value rises x% and then falls y% (or two rises).
Traditional. Multiply by (1+x/100) then (1±y/100).
Shortcut. Net % ≈ x + y + (xy)/100, with y negative for a fall. For +x then −x, net = −x²/100.
Do not use if the two bases are different quantities (price vs quantity) — that is not successive on the same base.
2. Percentage of a round number
10% = divide by 10. 5% = half of that. 1% = divide by 100. Build 12% as 10% + 1% + 1%.
Do not use on 17.5% of 847 if options sit 1–2 marks apart — finish the exact product.
3. Square of a number near 50 or 100
(100−a)² = 10000 − 200a + a². Example: 96² = 10000 − 800 + 16 = 9216.
(50+a)² = 2500 + 100a + a². Example: 53² = 2500 + 300 + 9 = 2809.
Do not use if you cannot keep the cross term; a missing 2ab is worse than a slow multiply.
4. Average speed for equal distances
If you go at u and return the same road at v, average = 2uv/(u+v), not (u+v)/2.
Do not use when the two legs have different distances — then it is total distance over total time only.
5. Two-discount equivalent
d1 and d2 become d1 + d2 − d1d2/100.
Do not use for a discount plus a GST (tax is on the discounted SP, a different base).
6. HCF × LCM identity
For two integers, product = HCF × LCM. Fast when one number and both HCF/LCM are given.
Do not use on three numbers without extra information.
Practice these chapters next
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.
