CAT 2025 Lesson : Interpretative Tables - Case 3

Details for Questions 10 to 13 are provided below

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


[CAT 2017 S2]

10) How many Thin Crust pizzas were to be delivered to Party 3?

(1) 398
(2) 162
(3) 196
(4) 364
11) How many Normal Cheese pizzas were required to be delivered to Party 1?

(1) 104
(2) 84
(3) 16
(4) 196

12) For Party 2, if 50% of the Normal Cheese pizzas were of Thin Crust variety, what was the difference between the numbers of T-EC and D-EC pizzas to be delivered to Party 2?

(1) 18
(2) 12
(3) 30
(4) 24

13) 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?

(1) Rs. 59480
(2) Rs. 59840
(3) Rs. 42520
(4) Rs. 45240

Solution

Case Solution

The total Pizzas delivered to Party 3 is 70%, which is 560 pizzas. And the remaining 240 Pizzas are equally divided between Party 1 and Party 2. This means that each Party got 120 Pizzas.


By using the above table, we can form a table with the total for each Thin Crust, Deep Dish, Normal Cheese and Extra Cheese Pizza.

Total Thin Crust Pizzas = 0.375 $\times$ Total = 300, so Total Deep Dish Pizzas = 500.

Total Normal Cheese Pizzas = 0.52 $\times$ Total = 416, so Total Extra Cheese Pizzas = 384.

Party 1 Thin Crust Pizza = 0.6 $\times$ Total Party 1 Pizza = 0.6 $\times$ 120 = 72, so Party 1 Deep Dish Pizza = 48.

Party 2 Thin Crust Pizza = 0.55 $\times$ Total Party 2 Pizza = 0.55 $\times$ 120 = 66, so Party 2 Deep Dish Pizza = 54.

Party 2 Normal Cheese Pizza = 0.3 $\times$ Total Party 2 Pizza = 0.3 $\times$ 120 = 36, so Party 2 Extra Cheese Pizza = 84.

Party 3 Normal Cheese Pizza = 0.65 $\times$ Total Party 3 Pizza = 0.65 $\times$ 560 = 364, so Party 2 Extra Cheese Pizza = 196.

With this, we can find Party 3’s Thin Crust and Deep Dish Pizzas and Party 1’s Normal Cheese and Extra Cheese Pizzas.



10)

We can answer based on the table below:



Party 3 Thin Crust Pizza = 162

Answer: (2) 162

11)

We can use the table in question 10 to solve this question as well.

Party 1 Normal Cheese Pizza = 16

Answer: (3) 16

12)

For Party 2, 50% of the Normal Cheese pizzas were of Thin Crust variety, which is 18 Pizzas. Then the remaining 18 Pizzas will be Deep Dish Normal Cheese Pizzas.

Thin Crust Extra Cheese Pizza = 66 – 18 = 48
Deep Dish Extra Cheese Pizza = 54 – 18 = 36



⇒ T-EC – D-EC = 48 - 36 = 12

Answer: (2) 12

13)

25% of the Normal Cheese Pizzas (which is 4) delivered to Party 1 were of Deep Dish variety. Then the Thin Crust Normal Cheese Pizzas will be 12.

Deep Dish Extra Cheese Pizza = 48 – 4 = 44
Thin Crust Normal Cheese Pizza = 72 – 12 = 60



Suppose 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 a T-EC pizza costs Rs. 500.

⇒ T-NC = D-NC = $\dfrac{3}{5}$ D-EC
⇒ D-EC = T-EC + 50, T-EC = 500

⇒ D-EC = 500 + 50 = 550

⇒ T-NC = D-NC = $\dfrac{3}{5} \times 550 = 330$



Answer: (1) Rs. 59480

Answer:
10) (2) 162
11) (3) 16
12) (2) 12
13) (1) Rs. 59480