Discussion

Question:

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

Explanation:

Now 70% of the pizzas were delivered to party 3 and the balance 30% of the pizzas were delivered to the remaining 2 parties i.e., Party 1 and Party 2. So each of Party 1 and Party 2 will receive

$\Rightarrow \frac{100-70}{100}\times \frac{1}{2}$ × 800 = 120 pizzas.

Party 3 will receive $\Rightarrow \frac{70}{100}$ × 800

= 560 pizzas.

Now number of Thin crust pizzas received by Party 1 = 0.6 × 120 = 72

So number of Deep dish pizzas received by Party 1 = 120 – 72 = 48

Similarly, number of Thin crust pizzas received by Party 2 = 0.55 × 120 = 66 and number of deep dish pizzas received by party 2 = 120 – 60 = 54

Number of normal cheese pizzas received by party 2 = 0.3 × 120 = 36

Number of extra cheese pizzas received by party 2 = 120 – 36 = 84

Now number of normal cheeze pizzas received by party 3 = 0.65 × 560 = 364

So number of extra cheese pizzas received by party 3 = 560 – 364 = 196

Now total number of Thin crust pizzas delivered to the 3 parties = 0.375 × 800

= 300

So, number of Deep Dish Pizzas delivered to the 3 parties = 800 – 416 = 384

So number of thin crust pizzas received by party B = 300 – (72 + 66) = 162 and number of deep dish pizzas received by party 3 = 500 – (48 + 54) = 398

Let number of thin crust normal cheese pizzas received by party 1, 2 and 3 be a, b and c.

Now number of deep dish normal cheese pizzas received by party 2 = 36 – b

So, the number of deep dish extra cheese pizzas received by party 2 = 54 – (36 – b) = 18 + b

Now total number of extra cheese deep dish pizzas received by party 3 = 196 – (162 – c) = 34 + c

Let number of deep pan normal cheese pizzas received by party 1 be ‘d’.

∴ Number of deep dish extra cheeze pizzas will be ‘48-d’

Now let us represent all this information in a table given below:

​​​​​​​

Now, number of normal cheese pizzas delivered to all parties is 416. Also total number of normal cheese pizzas delivered to party 1 = a + d

∴ 416 = a + b + c + d + 36 – b + 364 – c

416 = a + d + 400

⇒ a + d = 16.

Hence, option (c).

 

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