A set A consists of integers 27, 28, 30 and 33. If integer k is included in the set, the average of set A will increase by 30%. What is the value of integer k ?

Average of set A
= $$\frac{27 + 28 + 30 + 33}{4}$$
= $$\frac{118}{4}$$
= 29.5
After increase
= $$\frac{29.5 × 130}{100}$$
= 38.35
Now
$$\frac{{{\text{Sum of first four numbers + k}}}}{5}$$       $$ = {\text{New average}}$$
⇒ 118 + k = 38.35 × 5
⇒ 118 + k = 191.75
⇒ k = 191.75 - 118
⇒ k = 73.75