The average of the numbers a, b, c and d is 2d + 4. Also, the averages of the numbers a and b; b and c ; c and d are 8, 5 and 4, respectively, If e = a + d + 1, then what is the average of the numbers d and e?

7

Sum of a , b , c & d = 4 × ( 2d+4)  = 8d  + 16

a + b + c + d = 8d + 16  -----(1)

Sum of a& b = 2 × 8 = 16

Sum of b & c = 2 × 5 = 10

Sum of c & d = 2 × 4 = 8

Put sum of a & b OR c & d in equation 1

16 + 8 = 8d + 16

d = 1

a + 10 + 1 = 24

a = 13

e = 13 + 1 - 1 = 13

Average of e & d = \(\frac{13 + 1 }{2}\)  = 7