In mathematics there are two kinds of proportionalities as mentioned below,
Let us study each of them in some detail.
Y is said to be directly proportional to X if and only if their ratio is always constant.
But what does a constant ratio mean?
When we divide Y by X we should get some constant value every time. This constant value is called Proportionality constant. It is denoted by the letter ‘C’. Here if one of the value (here Y ) increases, then the other corresponding value (here X ) increases automatically as, the two values are interdependent.
Direct proportionality is expressed as
This equation can be written as
Where C is the proportionality constant.
For example,
If Y1 is directly proportional to X1 and Y2 is directly proportional to X2 then we can write,
If C1 = C2 =C then,
we can write,
Y is said to be inversely or indirectly proportional to X if their product is always constant.
And what does this constant ratio mean?
When we multiply Y with X we should get some constant value every time. This constant is called Proportionality constantT. This is also denoted by letter ‘C’. Here the increase or decrease in one of the value has no effect on the other value as, is one of the value increases, the other corresponding value increases automatically as, the two values are interdependent.
Inverse proportionality is expressed as
This equation can be written as
C is the proportionality constant.
For example,
If Y1 is inversely proportional to X1 & Y2 is inversely proportional to X2 then we can write,
If C1 = C2 =C, then we can write
TIME AND MEN
To complete the given work,
So here, Time taken to complete the work (T) and number of men required to complete the work (M) are inversely proportional
Hence, T1M1 = T2M2
EFFICIENCY AND TIME
To complete the given work,
So here, efficiency of workers (E) and Time taken to complete the work (T) are inversely proportional.
Hence, E1T1 = E2T2
EFFICIENCY AND MEN
To complete the given work,
So here, efficiency of workers (E) and Number of workers (M) are inversely proportional.
Hence, E1M1 = E2M2
WORK AND TIME, DAYS, MEN AND EFFICIENCY
Work is directly proportional to Men (M), Efficiency (E), Time (T) and Days (D)
Equation 1: If work is more then, time required to complete the work is more or If more time is given then, more work can be done (W α T)
This can be represented as,
W1T2=W2T1
Equation 2: If work is more number of days required to do the work are more or if number of days given are more then, more work can be done (W α D)
This can be represented as,
W1D2 =W2D1
Equation 3: If work is more no of men are more or If Men are more then, more work can be done (W α M)
This can be represented as,
W1M2=W2M1
Equation 4: If work is more then, efficiency should be more or If efficiency is more then, more work can be done (W α E)
This can be represented as,
W1E2=W2E1
Hence, on combining all the above four equation we can say,
W1T2D2M2E2 = W2T1D1M1E1
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