The average of five numbers is 36. The average of the first two numbers is 1.5 times that of the last three numbers. What is the sum of the first two numbers?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 90.
Let the five numbers be a, b, c, d, and e
We know that,
Average = Sum of observations/Number of observations
Sum of five numbers = a + b + c + d + e = 36 × 5 = 180.....(1)
Let the average of the last three numbers be x,
The sum = c + d + e = 3x.....(2)
The average of the first two numbers a and b is given as 1.5 times the average of the last three numbers
⇒ (a + b)/2 = 1.5x
⇒ a + b = 3x....(3)
Substitute eq 2 and 3 in eq 1
⇒ 3x + 3x = 180
⇒ 6x = 180
⇒ x = 30
Putting x in eq 3
⇒ a + b = 3 × 30
⇒ a + b = 90
Thus, the sum of the numbers is 90