some IQ formula

1. Finding the number of bench and students

- 1st condition : n = xb – extra bench X x

- 2nd condition : n = yb + extra students

- Where x = given no. of students in one bench for 1st condition

- Where y = given no. of students in one bench for 2nd condition

2. No. of days to climb

- N = (H-D)/(U-D)

- Where H = Height of the given things, U = Upward climbing and D = Downward 

3. Equation for having 2 Legs and 4 Legs

- 1st equation : Total no. of Head = x + y

- 2nd equation : Total no. of Legs = 2x + 4y

4. Series 

Arithmetic series Geometric series 

nth term = a + (n - 1)d nth term = arn-1 

5. Counting the number of squares 

- If nxn : no. of squares = n2 + (n-1)2 + (n-2)2 + (n-3)2 +....(n-n)2

- If mxn : no. of squares = n2 + (n-1)2 + (n-2)2 + (n-3)2 +...(n-n)2 + (m-n) (m-1)(m-2)(m-3)....(m-n)

6. Counting the Rectangles

= R(R+1) x C(C+1) x 1/4

7. Counting the triangles

- 

No. of triangle = 1 

No. of triangle = 2x1/2 = 3 

No. of triangle = base line = 4 

No. of triangle = base line x 3 = 4x3 = 12 

No. of triangle = no. of head x 3 = 2x 3 = 6 

No. of triangle = 4n – 3 = 4 x 3 – 3 = 9

8. Addition of natural number = n/2 x  (n+1)

9. No. of Shaking hand = n/2 x (n+1) 

10. Counting from Right hand side and Left hand side : T = R + L – 1 

11. Permutation = n!/(n-r)!

12. Combination = n! / (n-r!)r!

13. Calculation of distance : S = V x T (velocity x time) where V = (V1xV2x2)/(V1+V2)

14. h2  = p2 + b2 (formula of hypotenuse)

15. Simple interest (SI) = PTR/100

16. Compound Interest (CI) = P (1+r)t

17. Area of Rectangle = 2 (l + b)

18. Area of square = 4l

19. Area of four Wall of room = 2h (l x b)

20.  Area of Triangle = ½ x b x h 

21. Area of Triangle = (s(s-a)(s-b)(s-c))1/2 where s = (a+b+c)/2 and a,b,c = angle of triangle

22. Perimeter of Triangle = a+b+c

23. Equilateral triangle area = 31/3/4 x a2

24. Perimeter of Equilateral triangle area = 3a

25. Area of Parallelogram = b x h 

26. Area of Circle = 

27. Perimeter of Circle = 2

28. Volume of Cuboids = l x b x h

29. Surface Area of Cuboids = 2 (lb + lh + bh)

30. Volume of Cube = l3

31. Area of surface of Cube = 6l3

32. Volume of Cylinder = 

33. Curved surface Area of Cylinder =  2

34. Total surface Area of Cylinder = 

35. Volume of Sphere = 4/3  

36. Total surface area of sphere = 4 

37. Inductive Reasoning = Specific to Generalization

38. Deductive Reasoning = General to Specific

39. Water Images = Turned and Inverted Images

40. Mirror Images = Right hand side is shown in left hand side and vice versa

41. Embedded figure = Contain the same figure in complex figure

42. Directions : Clockwise and Anti-Clockwise

43. Eight  Direction : North, South, East, West, North-East, South- East, North-West, South-West 

44. Profit and Loss : 

- Profit = Sales Value – Cost Price

- Profit % = ( Sales Value – Cost Price ) / Cost Price

- Discount % = ( Marked Value – Sales Value ) / Marked Value