Answer:
The percentage increase in [tex]T[/tex] is 20 %.
Step-by-step explanation:
Let be [tex]T = \frac{k\cdot x}{y}[/tex], whose initial parameters are [tex]k = k_{o}[/tex], [tex]x = x_{o}[/tex] and [tex]y = y_{o}[/tex]. If these three parameters are increased by 20 %, then initial and final values of [tex]T[/tex] are, respectively:
Initial value
[tex]T_{i} = \frac{k_{o}\cdot x_{o}}{y_{o}}[/tex] (1)
Final value
[tex]T_{ii} = \frac{(1.2\cdot k_{o})\cdot (1.2\cdot x_{o})}{1.2\cdot y_{o}}[/tex]
[tex]T_{ii} = \frac{1.2\cdot k_{o}\cdot x_{o}}{y_{o}}[/tex] (2)
(1) in (2):
[tex]T_{ii} = 1.2\cdot T_{i}[/tex]
And the percentage increase in T is:
[tex]\%T = \frac{T_{ii}-T_{i}}{T_{i}}\times 100\,\%[/tex] (3)
[tex]\%T = \frac{1.2\cdot T_{i}-T_{i}}{T_{i}}\times 100\,\%[/tex]
[tex]\%T = 20\,\%[/tex]
The percentage increase in [tex]T[/tex] is 20 %.
