A function of two variables varies directly with x and inversely with y. Determine function when x = 5 and y = 3. Given that, for x = 0 and y = 1, f = 15 and for x = 1 and y = 15, f = 2.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 10.
f = k(x/y) where k is the constant of proportionality
When x = 1 and y = 15, f = 2
k(1/15) = 2 ⇒ k = 30
f ∝ x and f ∝ 1/y
⇒ f = k1x and f = k2/y
⇒ f = k1x + k2/y
For x = 0 and y = 1, f = 15 then, 15 = k1 × 0 + k2/1
⇒ k2 = 15
For x = 1 and y = 15, f = 2 then, 2 = k1 × 1 + 15/15
⇒ k1 = 1
For x = 5 and y = 3, f = 1 × 5 + 15/3 = 5 + 5 = 10
Hence, the required value is 10.