The average weight of A, B, C, and D is 33 kg. C is 12 kg lighter than A, while B is 6 kg heavier than C. D's weight is 10 kg less than that of C. What is the average weight of A and D?

The average weight of A, B, C, and D is 33 kg.

A+B+C+D = $$33\times4$$ = 132    Eq.(i)

C is 12 kg lighter than A.

C = A - 12

A = C+12    Eq.(ii)

While B is 6 kg heavier than C.

B = C+6    Eq.(iii)

D's weight is 10 kg less than that of C.

D = C-10    Eq.(iv)

Put Eq.(ii), Eq.(iii) and Eq.(iv) in Eq.(i).

C+12+C+6+C+C-10 = 132

4C+18-10 = 132

4C+8 = 132

C+2 = 33

C = 33-2

C = 31

The average weight of A and D = $$\frac{Eq.\left(ii\right)+Eq.\left(iv\right)}{2}$$

= $$\frac{C+12+C-10}{2}$$

= $$\frac{2C+2}{2}$$

= C+1

Put the value of 'C'.

= 31+1

= 32