Question

The average of six numbers is 30.if the average of first four is 25 and that of last three is 35, the fourth number is?

Answer 1

Let the 6 numbers be x1, x2, x3, x4, x5 and x6
Given average of 6 numbers = 30
Hence (x1+ x2 + x3 + x4 + x5 + x6)/6 = 30
Therefore, x1+ x2 + x3 + x4 + x5 + x6 = 180  → (1)
Similarly, average of first  numbers = 25
Hence (x1+ x2 + x3 + x4)/4 = 30
Therefore, x1+ x2 + x3 + x4 = 120  → (2)
Subtract (2) from (1) we get
x5 + x6 = 60 → (3)
It is also given that the average of last 3 numbers = 35
Hence (x4 + x5 + x6)/3 = 35
Therefore, x4 + x5 + x6 = 105 → (4)
Subtract (3) from (4), we get
x4 = 45
Thus the fourth number is 45.