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Now in order to calculate the cost of $1$ soap, we will divide $153.80$ by $12$. Therefore, we get

cost of $1$ soap $ = $ Rs. $\dfrac{{153.80}}{{12}}$.

Now in order to find the cost of $15$ soaps, we need to multiply the cost of $1$ soap with $15$. Therefore, we get cost of $15$ soaps $ = \left( {\dfrac{{153.80}}{{12}}} \right) \times 15$

$ \Rightarrow $ Cost of $15$ soaps $ = \left( {\dfrac{{153.80}}{4}} \right) \times 5$

$ \Rightarrow $ Cost of $15$ soaps $ = 38.45 \times 5$

$ \Rightarrow $ Cost of $15$ soaps $ = $ Rs. $192.25$

Therefore, if the cost of a dozen soaps is Rs. $153.80$ then the cost of $15$ such soaps is Rs. $192.25$.