The average of 4, 6, 8, 12 and x is 7 and the average of x, 9, 13, 15 and y is 9. What is the value of 2x - 3y?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 1
The average of 4, 6, 8, 12, and x is 7 and the average of x, 9, 13, 15, and y is 9.
Total = Average × Number of entities
There are 5 numbers in the series 4, 6, 8, 12, x.
According to the question -
4 + 6 + 8 + 12 + x = 7 × 5
30 + x = 35
x = 35 - 30
x = 5
There are 5 numbers in the series x, 9, 13, 15, y.
According to the question -
x + 9 + 13 + 15 + y = 9(5)
5 + 9 + 13 + 15 + y = 45 (∵ x = 5)
42 + y = 45
y = 45 - 42
y = 3
(2x - 3y) = (2 × 5 - 3 × 3) = 10 - 9 = 1