Question

D varies as R and S, and inversely as t. D=12, R=3, S=20, and t=5, find D when R=15, S=4 and t=8.

Answer 1

Given:

D varies as R and S, and inversely as t.

D=12, R=3, S=20, and t=5

To find:

The value of D when R=15, S=4 and t=8.

Solution:

It is given that D varies as R and S, and inversely as t. So,

$D\propto \dfrac{RS}{t}$

$D=\dfrac{kRS}{t}$                ...(i)

Where, k is the constant of proportionality.

We have, D=12, R=3, S=20, and t=5. Substituting these values in (i), we get

$12=\dfrac{k(3)(20)}{5}$

$12=12k$

$\dfrac{12}{12}=k$

$1=k$

Substituting $k=1$ in (i), we get the required equation.

$D=\dfrac{(1)RS}{t}$

$D=\dfrac{RS}{t}$

We need to find D when R=15, S=4 and t=8. Substituting R=15, S=4 and t=8 in the above equation, we get

$D=\dfrac{(15)(4)}{8}$

$D=\dfrac{60}{8}$

$D=7.5$

Therefore, the required value of D is 7.5.