Central Tendency & DispersionMTP May 19 Series IIQuestion 3156 of 473

If $\displaystyle X$ and $\displaystyle Y$ are related by $\displaystyle 2X+3Y=4$ and SD of $\displaystyle X$ is 6, then SD of $\displaystyle Y$ is

\displaystyle 22

\displaystyle 4

\displaystyle 40

\displaystyle 9

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Correct Answer

✅ Option b — $\displaystyle 4$

**Given:**

\displaystyle 2X + 3Y = 4

, SD of

\displaystyle X

= 6 **Step 1: Express

\displaystyle Y

in terms of

\displaystyle X

.**

3Y = 4 - 2X

Y = \frac{4 - 2X}{3} = \frac{4}{3} - \frac{2}{3}X

**Step 2: Use the property of SD for linear transformations.** For

\displaystyle Y = a + bX

\displaystyle SD(Y) = |b| \cdot SD(X)

Here

\displaystyle b = -\frac{2}{3}

, so:

SD(Y) = \left|{-\frac{2}{3}}\right| \times SD(X) = \frac{2}{3} \times 6 = 4

Hence, **Option B** is the correct answer.

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