SSC CPO Formula Sheet
Ten formulas, what each one is for, and a worked example.
SSC CPO Paper 1 quant covers the full SSC range: number system, arithmetic, algebra, geometry, mensuration and trigonometry, at a level close to CGL Tier 1.
These ten formulas round out the CGL and CHSL sheets with the topics CPO candidates most often miss, plus a worked successive-percentage example.
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The 10 Formulas
1
Formula
HCF × LCM
Expression
HCF × LCM = Product of the two numbers
Use it for
Finding a missing number from its HCF and LCM.
2
Formula
Successive percentage change
Expression
Net % = a + b + (a × b) ÷ 100
Use it for
Two changes in a row, such as a rise then a discount.
3
Formula
Partnership
Expression
Profit share ∝ Capital × Time
Use it for
Splitting profit between partners who invested for different periods.
4
Formula
Alligation (mixtures)
Expression
Cheaper : Dearer = (Dearer − Mean) : (Mean − Cheaper)
Use it for
Ratio in which two items are mixed to reach a mean price.
5
Formula
Boats and streams
Expression
Boat speed = (D + U) ÷ 2; Stream = (D − U) ÷ 2
Use it for
From downstream (D) and upstream (U) speeds.
6
Formula
Pipes and cisterns
Expression
Net fill per hour = 1/a − 1/b
Use it for
One pipe filling (a hours) while another empties (b hours).
7
Formula
Cone volume
Expression
V = (1/3)πr²h; Slant height l = √(r² + h²)
Use it for
Mensuration (3D).
8
Formula
Cuboid
Expression
Volume = l × b × h; Surface area = 2(lb + bh + hl)
Use it for
Boxes, rooms and tanks.
9
Formula
Pythagorean identities
Expression
sin²θ + cos²θ = 1; sec²θ − tan²θ = 1; cosec²θ − cot²θ = 1
Use it for
Trigonometry simplification.
10
Formula
Pythagoras theorem
Expression
Hypotenuse² = Base² + Height²
Use it for
Right triangles, heights and distances.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | HCF × LCM | HCF × LCM = Product of the two numbers | Finding a missing number from its HCF and LCM. |
| 2 | Successive percentage change | Net % = a + b + (a × b) ÷ 100 | Two changes in a row, such as a rise then a discount. |
| 3 | Partnership | Profit share ∝ Capital × Time | Splitting profit between partners who invested for different periods. |
| 4 | Alligation (mixtures) | Cheaper : Dearer = (Dearer − Mean) : (Mean − Cheaper) | Ratio in which two items are mixed to reach a mean price. |
| 5 | Boats and streams | Boat speed = (D + U) ÷ 2; Stream = (D − U) ÷ 2 | From downstream (D) and upstream (U) speeds. |
| 6 | Pipes and cisterns | Net fill per hour = 1/a − 1/b | One pipe filling (a hours) while another empties (b hours). |
| 7 | Cone volume | V = (1/3)πr²h; Slant height l = √(r² + h²) | Mensuration (3D). |
| 8 | Cuboid | Volume = l × b × h; Surface area = 2(lb + bh + hl) | Boxes, rooms and tanks. |
| 9 | Pythagorean identities | sin²θ + cos²θ = 1; sec²θ − tan²θ = 1; cosec²θ − cot²θ = 1 | Trigonometry simplification. |
| 10 | Pythagoras theorem | Hypotenuse² = Base² + Height² | Right triangles, heights and distances. |
Worked Example: Successive Percentage Change
A price rises by 20% and then falls by 10%. What is the net change?
- 1
Apply net % = a + b + ab/100
20 + (−10) + (20 × −10) ÷ 100.
- 2
Calculate
20 − 10 − 2 = 8.
- 3
Answer
A net increase of 8%, not 10%.
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Signs Matter in Successive Change
Enter a decrease as a negative number. The product term (a × b ÷ 100) is what makes a 20% rise and a 10% fall not cancel to 10%.
FAQs
Is SSC CPO maths the same as CGL?expand_more
The syllabus is close to CGL Tier 1, with the same topic list.
Is there maths in Paper 2?expand_more
No. Paper 2 is English language and comprehension.
Does HCF × LCM work for three numbers?expand_more
No. The product rule holds only for two numbers.
Next steps
Take a full SSC CPO mock testThe whole Paper I syllabus in one timed, scored paper.