Average age of A, B and C is 84 years. When D joins them the average age becomes 80 years. A new person, E, whose age is 4 years more than D, replaces A and the average of B, C, D and E becomes 78 years. What is the age of A ?

avg age of a,b,c = 84

$$\frac{A+B+C}{3}$$ = 84

A+B+C = 84*3 =252 ........................(1)

similarly , $$\frac{A+B+C+D}{4}$$ = 80

A+B+C+D = 80*4 = 320

so using (1)

252 + D = 320

D = 68 i.e, E = 72 (as mentioned in the question)................(2)

$$\frac{B+C+D+E}{4}$$ = 78

B+C+D+E = 78*4 = 312

using (2)

B+C+68+72 =312

B+C = 172 .................................(3)

put (3) in (1)

A = 80