# Three quantities R, S, and T are such that R varies directly as S and inversely as the square of...

## Question:

Three quantities R, S, and T are such that R varies directly as S and inversely as the square of T.

(a) Given that R = 480 when S = 150 and T = 5, write an equation connecting R, S, and T.

(b) (i) Find the value of R when S = 360 and T = 1.5.

(ii) Find the percentage change in R if S increases by 5% and T decreases by 20%.

## Proportionality

Proportionality is the relation between two varying quantities which are either in directly proportional or in inversely proportional. If they are connected to the constant i..e their ratio or product are constant then the value of the constant is known as coefficient of proportionality or also called proportionality constant

## Answer and Explanation:

Proportionality

According to question

{eq}R \propto \dfrac{S}{T} {/eq}

Now Above condition are converting into equation

We have

{eq}R = k\dfrac{S}{T} {/eq}

Now putting the value of the R=480 and S=150 and T=5 in above equation

we can find the value of k

{eq}\begin{align*} 480 = \dfrac{{k \times 150}}{5}\\ k = \dfrac{{480 \times 5}}{{150}}\\ k = 16 \end{align*} {/eq}

Now the the equation are ..

{eq}R = \dfrac{{16 \times S}}{T} {/eq}

According to 2nd condition

If S=360 and T=1.5

Then

{eq}\begin{align*} R = \dfrac{{16 \times S}}{T}\\ R = \dfrac{{16 \times 360}}{{1.5}}\\ R = 3840 \end{align*} {/eq}

Now according to 3rd condition

If we increase S by 5% and decreasing T by 20% then

For solving these we are taken the example 2nd condition

So

S=378 and T=1.2

Now

{eq}\begin{align*} R = \dfrac{{16 \times 378}}{{1.2}}\\ R = 5040 \end{align*} {/eq}

Now

Increment in the value of R=5040-3840=1200

Now

{eq}\begin{align*} \% \;{\rm{increment = }}\dfrac{{1200}}{{3840}} \times 100\\ = 31.25\% \end{align*} {/eq}