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Let he buys $n$ dozen of candies at Rs.$15$ a dozen and $n$ more dozen at Rs.$12$ a dozen.

The average cost of candies per dozen $ = \left(\frac{15+12}{2}\right) = \frac{27}{2} = \text{Rs.}\;13.50$ a dozen

By selling a dozen Rs.$16.50$, he will make a profit $ = 16.50-13.50 = \text{Rs.}\;3$ per dozen.

- $1$ dozen $\longrightarrow \text{Rs.}\;3$
- $2n$ dozen $\longrightarrow \text{Rs.}\;150$

$\Rightarrow 2n = \frac{150}{3} = 50$ dozens.

$\therefore$ Fifty dozen of candies he will buy altogether.

$\textbf{Short Method:}$ Using the allegation method.

- $1$ dozen $\longrightarrow \text{Rs.}\;4.5 – \text{Rs.}\;1.5$
- $1$ dozen $\longrightarrow \text{Rs.}\;3$
- Rs. $1 \longrightarrow \frac{1}{3}$ dozen
- Rs. $150 \longrightarrow \frac{1}{3}\times150$ dozen
- Rs. $150 \longrightarrow 50$ dozen

Correct Answer $:\text{A}$