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UPSC CDS 1 2020 Math Paper

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Question : 24 of 100

Marks: +1, -0

If x varies as yz, then y varies inversely as

xz
$\frac{x}{z}$
$\frac{z}{x}$
$\frac{1}{(xz)}$

Solution:

Concept:

Direct variation relationship and algebraic rearrangement.

Explanation:

Given

x \propto yz

.

This means

x = k \cdot y \cdot z

for some constant

k

.

Rewrite to isolate

y

:

y = \frac{x}{kz}

.

Hence

y \propto \frac{x}{z}

(direct proportion).

For inverse variation,

y \propto \frac{1}{\text{something}}

implies that something is

\frac{x}{z}

.

Therefore

y \propto \frac{1}{(x/z)} = \frac{z}{x}

.

Alternatively, from

x \propto yz

, we get

\frac{x}{z} \propto y

.

Taking reciprocals:

\frac{z}{x} \propto \frac{1}{y}

.

So

y

varies inversely as

\frac{z}{x}

.

Answer:

\frac{z}{x}

(Option C).

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