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 ?

A. 68

B. 79

C. 73.75

D. 75.25

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Solution(By Apex Team)

$$\begin{array}{l}\text{ Average of set }\mathrm{A}\\ =\Large\frac{27+28+30+33}{4}\\ =\Large\frac{118}{4}\\ =29.5\\ \text{ After increase }\\ =\Large\frac{29.5\times130}{100}\\ =38.35\\ \text{Now,}\\ \Large\frac{\text { Sum of first four numbers }+\mathrm{k}}{5}=\small\text { New average }\\ \Rightarrow 118+\mathrm{k}=38.35 \times 5\\ \Rightarrow 118+\mathrm{k}=191.75\\ \Rightarrow \mathrm{k}=191.75-118\\ \Rightarrow \mathrm{k}=73.75 \end{array}$$