Increase and Decrease in Ratio

If the number of teachers in a college is increased from 50 to 60. Then the ratio of new staff and old staff is

\begin{array}{*{20}{c}} {{\text{No}}{\text{. of new  staff}}}&{\text{:}}&{{\text{No}}{\text{. of old staff}}} \\ {{\text{60}}}&{\text{:}}&{{\text{50}}} \\  {\text{6}}&{\text{:}}&{\text{5}} \end{array}


 

\frac{{{\text{no}}{\text{.  of new staff}}}}{{{\text{no}}{\text{. of old staff}}}} = \frac{6}{5}


We say that, number of teachers has been increased in ratio 6 : 5. In other words, no. of new staff is \frac{6}{5} times the no. of old staff.
Hence \boxed{{\text{no}}{\text{. of new staff =  }}\frac{{\text{6}}}{{\text{5}}}{\text{ (no}}{\text{. of old staff)}}}
Rule:
To increase a no. “x”  we multiply x by an improper fraction.
           

\boxed{{\text{no}}{\text{. of new staff =  }}\frac{{\text{6}}}{{\text{5}}}{\text{ (no}}{\text{. of old staff)}}}


Similarly to decrease a no.  “x”  we multiply x by an proper fraction.
           

\boxed{{\text{no}}{\text{. of old staff =  }}\frac{{\text{6}}}{{\text{5}}}{\text{ (no}}{\text{. of new staff)}}}


e.g. (1) Increase Rs. 20 in ratio 6 : 5
New value = {\text{20 x }}\frac{{\text{6}}}{{\text{5}}} = 24
e.g. (2) Decrease 56 in ratio 7 : 8
New value =  {\text{56 x }}\frac{{\text{7}}}{{\text{8}}} = 49

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