Question : Among three numbers, the first is twice the second and thrice the third. If the average of these three numbers is 396, then what is the difference between the first and the third number?
Option 1: 594
Option 2: 448
Option 3: 432
Option 4: 453
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Correct Answer: 432
Solution :
Let the first number be $6x$, the second number be $3x$ and the third number $2x$.
The average of the three numbers = $\frac{6x+3x+2x}{3}=\frac{11x}{3}$
According to the question,
$\frac{11x}{3}=396$
$\therefore x=\frac{1188}{11}=108$
Difference between the first and the third number = $ 6x−2x=4x=4×108 = 432$
Hence, the correct answer is 432.
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