Question : Of the 3 numbers whose average is 22, the first is $(\frac{3}{8 })^{th}$ of the sum of the other 2. What is the first number?
Option 1: 16
Option 2: 20
Option 3: 22
Option 4: 18
Correct Answer: 18
Solution :
Let the first number, second number, and third number be $x, y$, and $z$ respectively.
Given: $x = \frac{3(y+z)}{8}$
⇒ $y+z = \frac{8x}{3}$
Now, the average of three numbers = 22
Sum of the numbers = 3 × 22 = 66
According to the question:
$x+y+z = 66$
Putting the value of $y+z$, we get:
$x+\frac{8x}{3} = 66$
$⇒11x = 66\times3$
$\therefore x = 18$
Hence, the correct answer is 18.
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