The averages of 3 different data D1, D2, D3, are 30, 40, 50 respectively. If the average of D1 and D2 together is 38 and that of D2 and D3 together is 42, then the average of the three data D1, D2 and D3 together is

Given:

Average of D1 = 30

Average of D2 = 40

Average of D3 = 50

Average of D1 and D2 = 38

Average of D2 and D3 = 42

Formula used:

Average = Sum / Number of Terms

Calculation:

Let number of elements in D1 = x, in D2 = y, in D3 = z

⇒ Total of D1 = 30x

⇒ Total of D2 = 40y

⇒ Total of D3 = 50z

Average of D1 and D2 = 38

⇒ (30x + 40y)/(x + y) = 38

⇒ 30x + 40y = 38x + 38y

⇒ y = 4x

Average of D2 and D3 = 42

⇒ (40y + 50z)/(y + z) = 42

⇒ 40y + 50z = 42y + 42z

⇒ z = y/4

Now y = 4x and z = y/4 = 4x/4 = x

Total of all data = 30x + 40 × 4x + 50x = 240x

Total number of elements = x + 4x + x = 6x

⇒ Average = 240x / 6x = 40

∴ The correct answer is 40