Quick Formula Revision

Return to MPT — Quantitative / Math.

Use this sheet to recall one key formula per topic. Open the linked topic for conditions, worked steps, and drills.

On this page

Arithmetic

1. Percentages

Part of a whole, expressed per hundred.

$$\text{Percentage}=\dfrac{\text{Part}}{\text{Whole}}\times100$$

2. Profit, Loss & Discount

Buying/selling price relationships.

$$\text{Profit}\%=\dfrac{SP-CP}{CP}\times100$$

3. Ratio & Proportion

Direct/inverse proportion, mean/third/fourth proportional, componendo-dividendo, partnership, age ratios.

$$a:b=c:d \iff ad=bc$$

4. Multiple & Inverse Ratios

Chaining ratios through a common term; inverse proportion.

$$\text{inverse of } a:b \;=\; \dfrac{1}{a}:\dfrac{1}{b} \;=\; b:a$$

5. Average

Mean and shortcuts for adding/removing a value.

$$\bar{x}=\dfrac{\sum x}{n}$$

6. Mixture & Alligation

Blending two quantities/prices to hit a target average.

$$q_1:q_2=(V_2-M):(M-V_1)$$

7. Simple Interest

Interest grows linearly with time.

$$SI=\dfrac{P\times R\times T}{100}$$

8. Compound Interest / Depreciation

Annual compounding shown below; use the correct rate and period count for other frequencies.

$$A=P\left(1+\dfrac{R}{100}\right)^{T}$$

9. Time & Work

Combine constant individual work rates for the same job.

$$\dfrac{1}{T}=\dfrac{1}{a}+\dfrac{1}{b}$$

10. Pipes & Cisterns

Same as Time & Work, but subtract the emptying rate.

$$R=R_{fill}-R_{empty}$$

11. Time, Speed & Distance

Core motion relationship plus unit conversion.

$$D=S\times T$$

12. Trains

Crossing poles, platforms, and other trains.

$$t=\dfrac{L+P}{v}$$

13. Boats & Streams

Downstream/upstream speed relationships.

$$v_d=u+v,\qquad v_u=u-v$$

14. Fractions

Add, subtract, multiply, divide, compare.

$$\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}$$

---

Algebra

15. Linear Equations

Solve two equations in two unknowns.

$$a_1x+b_1y=c_1,\qquad a_2x+b_2y=c_2$$

16. Quadratic Equations

Discriminant and the root formula.

$$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$

17. Exponents & Indices

Product, quotient, and power rules.

$$a^m\cdot a^n=a^{m+n},\qquad (a^m)^n=a^{mn}$$

18. Logarithms

Product, quotient, and power rules for logs.

$$\log_a(xy)=\log_a x+\log_a y$$

19. Algebraic Expressions

Expanding and factoring identities.

$$(a+b)^2=a^2+2ab+b^2$$

20. Inequalities

Same rules as equations, except flip the sign on negative multiply/divide.

$$-2x>6 \;\Longrightarrow\; x<-3$$

---

Geometry & Mensuration

21. Basic Geometry

For a right triangle, c is the hypotenuse.

$$a^2+b^2=c^2$$

22. Areas (2D Mensuration)

Triangle, circle, trapezium, rhombus.

$$A=\pi r^2$$

23. Volumes (3D Mensuration)

Cube, cylinder, sphere, cone.

$$V=\dfrac{4}{3}\pi r^3$$

---

Number System

24. Number System

LCM/HCF, divisibility, remainders.

$$LCM(a,b)\times HCF(a,b)=a\times b$$

---

Data & Statistics

25. Basic Statistics

Mean, median, mode, range.

$$\bar{x}=\dfrac{\sum x}{n}$$

26. Tables & Graphs Interpretation

Reading bar/line/pie charts.

$$\%=\dfrac{\text{part}}{\text{total}}\times100$$

---

Combinatorics & Probability

27. Permutations & Combinations

Order matters vs. order doesn't matter.

$${}^nP_r=\dfrac{n!}{(n-r)!},\qquad {}^nC_r=\dfrac{n!}{r!(n-r)!}$$

28. Arithmetic & Geometric Sequences

AP and GP nth-term and sum formulas.

$$a_n=a_1+(n-1)d,\qquad a_n=a_1\cdot r^{(n-1)}$$

29. Probability

Favorable over total outcomes, when outcomes are equally likely.

$$P(\text{event})=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}$$

---

Islamic Finance & Law (Pakistan-specific)

30. Zakat & Ushr

Apply 2.5% to eligible assets under the question's assumptions; Ushr uses the stated 10% or 5% rate.

$$\text{Zakat}=\text{Assets}\times2.5\%$$

31. Inheritance (Mirath / Wirasat)

Fixed shares are allocated first. The ratio below applies when sons and daughters share the residue together.

$$\text{Son}:\text{Daughter}=2:1$$

---