All the essential formulas for Percentage, Profit-Loss, SI/CI, Time-Work, Speed-Distance that appear repeatedly in SSC CGL and CHSL exams.
1. X% of Y = (X × Y) / 100 2. % change = [(New - Old) / Old] × 100 3. If A is x% more than B: A = B × (100+x)/100 4. Successive % change: Net% = a + b + ab/100
5. Profit% = (Profit/CP) × 100 6. SP = CP × (100+Profit%)/100 7. CP = SP × 100/(100+Profit%) 8. Discount% = (Marked Price - SP)/Marked Price × 100 9. If two articles sold at same SP, one at x% profit and other at x% loss: Net Loss% = x²/100
10. SI = (P × R × T) / 100 11. CI = P[(1 + R/100)^T - 1] 12. CI - SI (2 years) = P(R/100)² 13. Effective Rate for CI half-yearly: (1 + R/200)² - 1
14. If A does in 'a' days, B in 'b' days: Together = ab/(a+b) 15. A is x times efficient as B → A takes time T/x if B takes T 16. Work = Efficiency × Time
17. D = S × T 18. Average speed (equal distance) = 2S1S2/(S1+S2) 19. Relative speed (same direction) = |S1 - S2| 20. Relative speed (opposite) = S1 + S2
21. If A:B = m:n and B:C = p:q → A:B:C = mp:np:nq 22. Componendo-Dividendo: (a+b)/(a-b) = (c+d)/(c-d)
23. Alligation Rule: Cheaper : Costlier = (Mean - Cheaper):(Costlier - Mean)
24. Area of Triangle = ½ × base × height = √[s(s-a)(s-b)(s-c)] 25. Area of circle = πr²; Circumference = 2πr 26. Area of trapezoid = ½(a+b)h 27. Diagonal of square = a√2; Diagonal of rectangle = √(l²+b²)
28. Volume of Cylinder = πr²h; CSA = 2πrh 29. Volume of Cone = ⅓πr²h; Slant height l = √(r²+h²) 30. Volume of Sphere = (4/3)πr³; SA = 4πr²
31. Divisibility by 3: Sum of digits divisible by 3 32. Divisibility by 9: Sum of digits divisible by 9 33. Divisibility by 11: (Sum of odd-position digits) - (Sum of even-position) divisible by 11 34. LCM × HCF = Product of two numbers
35. Mean = Sum of observations / Number 36. Median (odd n) = [(n+1)/2]th term 37. Mode = most frequent value 38. Range = Max - Min 39. Variance = Σ(x-x̄)²/n; SD = √Variance
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