Inverse Proportion

Two quantities a and b are said to be in Inverse proportion if

  1. Increase in a decreases the value of b
  2. Decrease in a increases the value of b

But the ratio of their respective values must be the same.

  • a and b will be in inverse proportion if k= ab
  • In such a case if b1, b2 are the values of b corresponding to the values a1, a2 of a respectively then, a1b1 = a2b2 = k
  • When two quantities a and b are in inverse proportion then they are written as a  \propto \mathrm{\dfrac{1}{b}}

Example

If 15 artists can make a statue in 48 hours then how many artists will be required to do the same work in 30 hours?

Solution:

Let the number of artists required to make a statue in 30 hours be y.

Number of hours4830
Number of artists15y

We know that as the no. of artists will increase the time to complete the work will reduce. So, the number of hours and number of artists are in inverse proportion.

So \mathrm{48\times15=30\times y\ (a_1b_1=a_2b_2)}

Therefore,

\text y=\dfrac{48\times15}{30}=24

So, 24 artists will be required to make the statue in 30 hours.

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