A variable W varies partly as M and Partly inversely as P. Which of the following correctly represents the relation with k$_1$ and k$_2$ constants?

Analyze the question

"Partly varies as M and partly inversely as P" is a partial variation (joint of two parts added together). We need the form that adds a direct-variation term and an inverse-variation term.

Concept

• W varies directly as M: W ∝ M, so W = k₁M
• W varies inversely as P: W ∝ 1/P, so W = k₂/P
• "Partly... and partly..." means the two parts are added:

W = k₁M + k₂/P

Checking the options

• A. W = k₁M/(k₂P): this is a single product/quotient (joint variation), not a sum. ✗
• B. W = (k₁ + k₂)M/P: this makes W vary directly as M and inversely as P together, with one combined constant. ✗
• C. W = k₁M + k₂/P: a direct part plus an inverse part, each with its own constant. ✓
• D. W = (k₁ + k₂)M + P: P appears directly with no constant, and there is no inverse variation. ✗

Exam tip: The word "partly" signals addition of terms, each with its own constant. Words like "jointly" signal multiplication instead. For example, "partly constant and partly varies as x" gives y = k₁ + k₂x.