Ratio
What is ratio ?
Suppose x and y are two quantities . The quotient a/b is called ratio . Ratio does not have any units.
What is compound ratio ?
Example : compound ratio of 2:5 and 4:7 is 2x4:5x7 = 8:35
What is duplicate ratio ?
Compound ratio of two equal ratio is called duplicate ration
Duplicate ratio of a:b = axa : bxb
Question :
If x:y=4:5 find value of (6x+4y) : (3x+6y).
Solution :
x/y = 4/5
(6x+4y):(3x+6y)
(6(x/y) + 4 ) : (3(x/y)+6 Divide numerator and denominator by y
Therefore , 6*4/5 + 4 : 3*4/5 + 6 = 44:42 = 22:21
Answer = 22:21
Algebra
Expansion formula
- (a + b)^2 = a^2 + 2ab + b^2
- (a - b)^2 = a^2 - 2ab + b^2
- (a + b) (a - b) = a^2 - b^2
- (x + a) (x + b) = x^2 + (a + b)x + ab.
- (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac
- (a + b)63 = a^3 + b^3 + 3ab (a + b) = a^3 + 3a^2b + 3ab^2 + b^3
- (a - b)^3 = a^3 - b^3 - 3ab (a - b) = a^3 - 3a^2b + 3ab^2 - b^3
