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Question:

Suppose that a T-NC pizza cost as much as a D-NC pizza, but 3/5th 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?

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 ⇒ $\frac{70}{100}$ × 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:

​​​​​​​

Let the price of a T-NC pizza and D-NC pizza be Rs ‘3x’. So, the price of a D-EC pizza will be ‘5x’ and the price of T-EC pizza will be Rs. ‘5x – 50’

Now 5x – 50 = 500 ⇒ 5x = 550 or x = 110

So the price of T-NC and D-NC pizza will be 3 × 110 or Rs. 330

Further, the price of D-NC pizza will be Rs. 550 and that of T-EC pizza will be Rs. 500

Now $\frac{d}{a+d}=\frac{1}{4}$⇒ 3d = a

Given a + d = 16 ⇒ 4d = 16 or d = 4

∴ a = 16 – 4 = 12

So total number of T-NC, T-EC, D-NC and D-EC pizzas, delivered to party 1 is 12, 60, 4 and 44 respectively.

Cost of pizzas to party 1 is calculated as below

Cost of T-NC pizzas = 12 × 330 = 3960

Cost of D-NC pizzas = 4 × 300 = 1320

Cost of T-EC pizzas = 60 × 500 = 30000

Cost of D-EC pizzas = 44 × 550 = 24200

Total cost = 3960 + 1320 + 30000 + 24200 = Rs. 59480.

Hence, option (a).