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NIMCET 2008 — Reasoning PYQ

NIMCET | Reasoning | 2008

Of the three numbers, second is twice the first and is also thrice the third. If the average of three numbers is 44, the largest number is

Choose the correct answer:

Explanation

To find the largest number, we first establish a relationship between the three numbers using a common variable.

Step 1: Define the Numbers

Let the three numbers be $x$ , $y$ , and $z$ .

According to the question:

The second number ( $y$ ) is twice the first ( $x$ ): $y = 2x \implies x = \frac{y}{2}$

The second number ( $y$ ) is thrice the third ( $z$ ): $y = 3z \implies z = \frac{y}{3}$

Step 2: Use the Average Formula

The average of three numbers is given as 44. The formula for average is:

$\text{Average} = \frac{x + y + z}{3}$

Substituting the value of the average:

$44 = \frac{\frac{y}{2} + y + \frac{y}{3}}{3}$

Step 3: Solve for $y$

Multiply both sides by 3:

$44 \times 3 = \frac{y}{2} + y + \frac{y}{3}$

$132 = \frac{3y + 6y + 2y}{6}$

$132 = \frac{11y}{6}$

Now, isolate $y$ :

$y = \frac{132 \times 6}{11}$

$y = 12 \times 6$

$y = 72$

Step 4: Find the other numbers

First number ( $x$ ) = $\frac{72}{2} = 36$

Second number ( $y$ ) = $72$

Third number ( $z$ ) = $\frac{72}{3} = 24$

Comparing the three numbers ( $36, 72, 24$ ), the largest number is 72.

Final Answer:

The largest number is 72.

Correct Option: (c)

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