Concept: Ratio Proportion, Variation & Partnership Quick Revision
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CONTENTS
Ratio is used to compare 2 or more similar quantities (expressed in same units). It is usually expressed in simplest form, i.e., common factor (if any) is eliminated.
If = , it means For every p parts of a, there are q parts of b.
If = , then a = p × x and b = q × x
where x is the common multiple.
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If = and a + b = T, then a = × T, and b = × T
If a × x = b × y, then =
If = = , then a : b : c = x : y : z
Note: Ratio of numerators is same as ratio of denominators
If a × x = b × y = c × z, then a : b : c = : :
If a : b = : , then to simplify RHS, we multiply all terms in RHS with LCM of denominators i.e., LCM (x, y)
Inverse or reciprocal ratio of a, b and c = : :
Note: If a question involves multiple ratios, their common factor need not be same.
Note, here ≠
If a, b, c and d are in proportion, then
⇒ =
⇒ a × d = c × bIf a, b and c are in continuous proportion, then
⇒ =
⇒ a × c = c2
If x is directly proportional to y, then
⇒ x ∝ y,
⇒ x = ky
⇒ = k (constant)
⇒ =
Note: When 2 quantities are directly proportional, their ratio is constant
If x is inversely proportional to y, then
⇒ x ∝ 1/y,
⇒ x = k/y
⇒ x × y = k (constant)
⇒ x1 × y1 = x2 × y2
Note: When 2 quantities are inversely proportional, their product is constant
If x is proportional to two or more variable, then it is proportional to product of all those variables.
Example: If x directly proportional to p and q while inversely proportional to r, then
x ∝
⇒ =
Let PA, IA and TA represent the Profit, Investment and Time invested for A [Same goes for B and C]
PA : PB : PC = IA × TA : IB × TB : IC × TC
PA : PB = (IA1 × TA1 + IA2 × TA2 + ...) : (IB1 × TB1 + IB2 × TB2 + ...)