Question

Given that T=KX/Y,find the percentage increase in T when k, xandy all increase by 20%​

Answer 1

Answer:

The percentage increase in $T$ is 20 %.

Step-by-step explanation:

Let be $T = \frac{k\cdot x}{y}$, whose initial parameters are $k = k_{o}$, $x = x_{o}$ and $y = y_{o}$. If these three parameters are increased by 20 %, then initial and final values of $T$ are, respectively:

Initial value

$T_{i} = \frac{k_{o}\cdot x_{o}}{y_{o}}$ (1)

Final value

$T_{ii} = \frac{(1.2\cdot k_{o})\cdot (1.2\cdot x_{o})}{1.2\cdot y_{o}}$

$T_{ii} = \frac{1.2\cdot k_{o}\cdot x_{o}}{y_{o}}$ (2)

(1) in (2):

$T_{ii} = 1.2\cdot T_{i}$

And the percentage increase in T is:

$\%T = \frac{T_{ii}-T_{i}}{T_{i}}\times 100\,\%$ (3)

$\%T = \frac{1.2\cdot T_{i}-T_{i}}{T_{i}}\times 100\,\%$

$\%T = 20\,\%$

The percentage increase in $T$ is 20 %.