Question : Among three numbers, the first is twice the second and thrice the third. If the average of these three numbers is 198, what is the difference between the first and the third numbers?
Option 1: 216
Option 2: 297
Option 3: 661
Option 4: 431
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Correct Answer: 216
Solution :
Let the first number be $6x$, the second number be $3x$, and the third number $2x$.
The average of the three numbers $= \frac{6 x+3x+2x}{3}= \frac{11x}{3}$
According to the question,
$\frac{11x}{3}=198$
$⇒11x=594$
$\therefore x=54$
The difference between the first and the third number $=(6x−2x)=4x=4×54=216$
Hence, the correct answer is 216.
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