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Suppose that r varies directly with s and inversely with t, and r = 2 when s = 3 and t = 12. What is the value of r when s = 5 and t = 4?

A2/5

B.32/5

C.10

D.20

Verified Answer :

taskmasters

The statement suppose that r varies directly with s and inversely with t is best represented as:

r α s/t

To make it into equality, we insert a proportionality constant, k:

r = ks/t

Using the initial conditions, we solve for k.

r = ks/t
r = 2 when s = 3 and t = 12

2 = k(3)/12
k = 8

Thus, when s = 5 and t = 4,

r = 8(5)/4
r = 10 -----> OPTION C

A correct option is an option (c)

Given values are,

\(r = 2\) when \(s = 3 , t = 12\)

According to the given question, the relation is,

\(r\propto \frac{s}{t}\\r=k\frac{s}{t}...(1)\)

Substituting the values \(r = 2\) when \(s = 3 , t = 12\) into equation (1)

\(2=\frac{3k}{12} \\k=\frac{24}{3} \\k=8\)

Since we have to find the value \(r\) again from equation (1)

\(r=\frac{8\times5}{4} \\r=10\)

So, the required value r is 10.

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