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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:

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

Suppose that a $T-NC$ pizza cost as much as a $D-NC$ pizza, but $3/5$th of the price of a $D-EC$ pizza. A $D-EC$ pizza costs Rs. $50$ more than a $T-EC$ pizza, and the latter costs Rs. $500$.

If $25\%$ of the Normal Cheese pizzas delivered to Party $1$ were of Deep Dish variety, what was the total bill for Party$1$?

  1. Rs. $59480$
  2. Rs. $59840$
  3. Rs. $42520$
  4. Rs. $45240$
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