# 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

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.

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

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 =  ${\text{56 x }}\frac{{\text{7}}}{{\text{8}}} = 49$