Correct Answer - Option 1 : 366.7
Given
Average of four number = 20
Formula used
Average = Sum of observation/No. of observation
(a + b + c + d)2 = a2 + b2 + c2 + d2 + 2(ab + bc + cd + da + bd + ac)
Calculation
Let the number be p, q, r, s
Sum of observation = 20 × 4 = 80
⇒ p + q + r + s = 80
Sum of their squares = 500 × 4 = 2000
⇒ p2 + q2 + r2 + s2 = 2000
⇒ 6400 = 2000 + 2(ab + bc + cd + da + bd + ac)
⇒ ab + bc + ca + da + bd + ac = 2200
Average of their products taken two at a time = 2200/6 = 366.7
∴ The required answer is 366.7