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Funky Pizzaria was required to supply pizzas to three different parties. The total number of pizzas it had to deliver was $800$, $70\%$ of which were to be delivered to Party $3$ and the rest equally divided between Party $1$ and Party $2$.

Pizzas could be of Thin Crust $(T)$ or Deep Dish $(D)$ variety and come in either Normal Cheese $(NC)$ or Extra Cheese $(EC)$ versions. Hence, there are four types of pizzas: $T-NC$, $T-EC$, $D-NC$ and $D-EC$. Partial information about proportions of $T$ and $NC$ pizzas ordered by the three parties is given below:

$\begin{array}{cccc}  & \text{Thin Crust (T)} & \text{Normal Cheese (NC)} \\ \text{Party 1} & 0.6 & -  \\ \text{Party 2}  & 0.55 & 0.3 \\ \text{Party 3} & - & 0.65  \\ \text{Total }& 0.375 & 0.52  \end{array}$

How many Normal Cheese pizzas were required to be delivered to Party $1$?

  1. $104$
  2. $84$
  3. $16$
  4. $196$
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