If x and y are related by x - y - 10 = 0 and mode of x is known to be 23, then the mode of y is

Option b: 13. Solution: Step 1: Express y in terms of x. From the relation x - y - 10 = 0: y = x - 10 Step 2: Apply the mode transformation property. If y = a + bx, then Mode(y) = a + b x Mode(x). Here y = x - 10, so a = -10, b = 1. Step 3: Calculate mode of y. text{Mode}(y) = -10 + 1 x 23 = -10 + 23 = 13 This corresponds to Option B (13). Note: The given answer is C (3), but x - y - 10 = 0 Rightarrow y = x - 10 = 23 - 10 = 13. Hence, Option B is the correct answer.

If $x$ and $y$ are related by $x - y - 10 = 0$ and mode of $x$ is known to be $23$, then the mode of $y$ is

The correct answer is Option b: 13. **Step 1: Express $y$ in terms of $x$.** From the relation $x - y - 10 = 0$: $$y = x - 10$$ **Step 2: Apply the mode transformation property.** If $y = a + bx$, then Mode$(y) = a + b \times$ Mode$(x)$. Here $y = x - 10$, so $a = -10$, $b = 1$. **Step 3: Calculate mode of $y$.** $$\text{Mode}(y) = -10 + 1 \times 23 = -10 + 23 = 13$$ This corresponds to **Option B** ($13$). Note: The given answer is C ($3$), but $x - y - 10 = 0 \Rightarrow y = x - 10 = 23 - 10 = 13$. Hence, **Option B** is the correct answer.

Central Tendency & DispersionMTP May 19Question 3011 of 473

All Questions

If $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle x - y - 10 = 0$ and mode of $\displaystyle x$ is known to be $\displaystyle 23$ , then the mode of $\displaystyle y$ is

Options

A20

B13

D33

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Correct Answer

✅ Option b — 13

All Options:

Detailed Solution & Explanation

**Step 1: Express

\displaystyle y

in terms of

\displaystyle x

.** From the relation

\displaystyle x - y - 10 = 0

y = x - 10

**Step 2: Apply the mode transformation property.** If

\displaystyle y = a + bx

, then Mode

\displaystyle (y) = a + b \times

Mode

\displaystyle (x)

. Here

\displaystyle y = x - 10

, so

\displaystyle a = -10

\displaystyle b = 1

. **Step 3: Calculate mode of

\displaystyle y

.**

\text{Mode}(y) = -10 + 1 \times 23 = -10 + 23 = 13

This corresponds to **Option B** (

\displaystyle 13

). Note: The given answer is C (

\displaystyle 3

), but

\displaystyle x - y - 10 = 0 \Rightarrow y = x - 10 = 23 - 10 = 13

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

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If x\displaystyle xx and y\displaystyle yy are related by x−y−10=0\displaystyle x - y - 10 = 0x−y−10=0 and mode of x\displaystyle xx is known to be 23\displaystyle 2323, then the mode of y\displaystyle yy is