Question : Of the three numbers whose average is 40, the first is $\frac{1}{3}$rd of the sum of the other two. What is the first number?
Option 1: 20
Option 2: 50
Option 3: 25
Option 4: 30
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Correct Answer: 30
Solution : Let the numbers be $x, y, z$. Their average is 40. Sum = $x + y + z = 40 × 3 = 120$ --(1) and given that $x = \frac{1}{3}(y+z)$ ⇒ $3x = y + z$ Putting the value of $y+z$ in equation 1, we get, $x + y + z = 120$ ⇒ $ x + 3x = 120$ ⇒ $4x = 120$ $\therefore x = 30$ Hence, the correct answer is 30.
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