A,B, C and D are four positive numbers such that A is $\frac{3}{4}$ times of B, B is $\frac{4}{5}$ times of C, and C is $\frac{3}{8}$ times of D. If the average of 4 times of A and 7 times of D is 316, then the average of all the four numbers A, B, C and D is:

38

A : B : C : D

3 : 4

   : 4 : 5

   :    : 3 : 8

9 : 12 : 15 : 40

⇒ According to the question,

The average of 4 times of A and 7 times of D is 316,

⇒ \(\frac{4(9) + 7(40)}{2}\)x = 316

⇒ \(\frac{316}{2}\)x = 316

⇒ x = 2,

The average of all the four numbers A, B, C and D,

⇒ \(\frac{9+12+15+40}{4}\) = \(\frac{76}{4}\) = 19x = 19 x 2 = 38.