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SET 1 — 🔍 CAT Level - CAT 2017
Funky Pizzeria 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)
Normal Cheese (NC) or Extra Cheese (EC)
Hence, there are four types of pizzas:
T-NC
T-EC
D-NC
D-EC
Partial information about proportions of Thin Crust (T) and Normal Cheese (NC) pizzas ordered by the three parties is given below:
Party 1: 60% of the pizzas ordered were Thin Crust (T). Information about the proportion of Normal Cheese (NC) pizzas is not provided.
Party 2: 55% of the pizzas ordered were Thin Crust (T) and 30% were Normal Cheese (NC).
Party 3: 65% of the pizzas ordered were Normal Cheese (NC). Information about the proportion of Thin Crust (T) pizzas is not provided.
Overall (all parties combined):
37.5% of the pizzas were Thin Crust (T).
52% of the pizzas were Normal Cheese (NC).
Question 1
How many Thin Crust pizzas were to be delivered to Party 3?
A. 398
B. 162
C. 96
D. 364
Question 2
How many Normal Cheese pizzas were required to be delivered to Party 1?
A. 104
B. 84
C. 16
D. 196
Question 3
For Party 2, if 50% of the Normal Cheese pizzas were of Thin Crust variety, what was the difference between the number of T-EC and D-EC pizzas to be delivered to Party 2?
A. 18
B. 12
C. 30
D. 24
Question 4
Suppose that a T-NC pizza costs 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?
A. Rs. 59480
B. Rs. 59840
C. Rs. 42520
D. Rs. 45240
SET 2 — CAT Level - CAT 2017
An old woman had the following assets:
(a) Rs. 70 lakh in bank deposits
(b) 1 house worth Rs. 50 lakh
(c) 3 flats, each worth Rs. 30 lakh
(d) Certain number of gold coins, each worth Rs. 1 lakh
She wanted to distribute her assets among her three children; Neeta, Seeta and Geeta.
The house, any of the flats or any of the coins were not to be split. That is, the house went entirely to one child; a flat went to one child and similarly, a gold coin went to one child.
Question 5
Among the three, Neeta received the least amount in bank deposits, while Geeta received the highest. The value of the assets was distributed equally among the children, as were the gold coins.
How much did Seeta receive in bank deposits (in lakhs of rupees)?
A. 30
B. 40
C. 20
D. 10
Question 6
Among the three, Neeta received the least amount in bank deposits, while Geeta received the highest. The value of the assets was distributed equally among the children, as were the gold coins.
How many flats did Neeta receive?
(Answer to be entered)
Question 7
The value of the assets distributed among Neeta, Seeta and Geeta was in the ratio of 1 : 2 : 3, while the gold coins were distributed among them in the ratio of 2 : 3 : 4.
One child got all three flats and she did not get the house.
One child, other than Geeta, got Rs. 30 lakh in bank deposits.
How many gold coins did the old woman have?
A. 72
B. 90
C. 180
D. 216
Question 8
The value of the assets distributed among Neeta, Seeta and Geeta was in the ratio of 1 : 2 : 3, while the gold coins were distributed among them in the ratio of 2 : 3 : 4.
One child got all three flats and she did not get the house.
One child, other than Geeta, got Rs. 30 lakh in bank deposits.
How much did Geeta get in bank deposits (in lakhs of rupees)?
(Answer to be entered)
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✅ Answers & Explanations
Set 1
Base data
Total pizzas = 800
Party 3 = 70% = 560
Party 1 = 120
Party 2 = 120
Question 1
Thin Crust pizzas for Party 3
Total Thin Crust = 37.5% of 800 = 300
Party 1 Thin Crust = 60% of 120 = 72
Party 2 Thin Crust = 55% of 120 = 66
Party 3 Thin Crust = 300 - 72 - 66 = 162
Answer: B. 162
Question 2
Normal Cheese pizzas for Party 1
Total NC = 52% of 800 = 416
Party 2 NC = 30% of 120 = 36
Party 3 NC = 65% of 560 = 364
Party 1 NC = 416 - 36 - 364 = 16
Answer: C. 16
Question 3
Difference between T-EC and D-EC for Party 2
Party 2 NC = 36
50% of NC are Thin Crust, so T-NC = 18
Party 2 total Thin Crust = 66
So T-EC = 66 - 18 = 48
Total EC = 120 - 36 = 84
D-EC = 84 - 48 = 36
Difference = 48 - 36 = 12
Answer: B. 12
Question 4
Total bill for Party 1
T-EC = Rs. 500
D-EC = Rs. 550
T-NC = D-NC = 3/5 of 550 = Rs. 330
Party 1 NC = 16
25% of NC are Deep Dish: D-NC = 4, T-NC = 12
Party 1 Thin Crust = 72, so T-EC = 72 - 12 = 60
Remaining D-EC = 120 - 12 - 4 - 60 = 44
Total bill = 12×330 + 4×330 + 60×500 + 44×550
= 3960 + 1320 + 30000 + 24200
= Rs. 59480
Answer: A. Rs. 59480
Set 2
Total non-gold assets = Bank deposits + House + Flats
= 70 + 50 + 90
= 210 lakhs
The total value was distributed equally among 3 children. Gold coins were also distributed equally.
So, the remaining non-gold assets must also be equal.
Each child’s non-gold share = 210 ÷ 3 = 70 lakhs
Now property values:
House = 50 lakhs
Each flat = 30 lakhs
Bank money will adjust the balance to make each child’s total 70 lakhs.
Possible distribution:
Neeta gets 2 flats = 60 lakhs
So bank deposit = 70 - 60 = 10 lakhs
Seeta gets house = 50 lakhs
So bank deposit = 70 - 50 = 20 lakhs
Geeta gets 1 flat = 30 lakhs
So bank deposit = 70 - 30 = 40 lakhs
This satisfies the condition:
Neeta received least bank deposit = 10
Geeta received highest bank deposit = 40
So:
5th Answer: C. 20
6th Answer: 2 flats
Let the gold coins be distributed in the ratio:
Neeta : Seeta : Geeta = 2 : 3 : 4
So coins are:
Neeta = 2x
Seeta = 3x
Geeta = 4x
Total gold coins = 9x
Total assets = Bank + House + Flats + Gold coins
= 70 + 50 + 90 + 9x
= 210 + 9x
The total asset value ratio is:
Neeta : Seeta : Geeta = 1 : 2 : 3
Total ratio parts = 6
So each part = (210 + 9x) ÷ 6
= 35 + 1.5x
Therefore:
Neeta’s total value = 35 + 1.5x
Seeta’s total value = 70 + 3x
Geeta’s total value = 105 + 4.5x
Now subtract gold coins:
Neeta’s non-gold value = 35 + 1.5x - 2x = 35 - 0.5x
Seeta’s non-gold value = 70 + 3x - 3x = 70
Geeta’s non-gold value = 105 + 4.5x - 4x = 105 + 0.5x
One child got all 3 flats = 90 lakhs and did not get the house.
Only Geeta can get all 3 flats because her non-gold value is more than 90.
So Geeta gets flats worth 90 lakhs.
The house must go to Seeta because Neeta’s non-gold value is less than 50.
So:
Seeta gets house = 50 lakhs
Seeta’s total non-gold value = 70 lakhs
So Seeta’s bank deposit = 20 lakhs
Now the child other than Geeta who got 30 lakhs in bank deposits must be Neeta.
Neeta’s bank deposit = 30
So:
35 - 0.5x = 30
0.5x = 5
x = 10
Total gold coins = 9x = 9 × 10 = 90
Geeta’s non-gold value = 105 + 0.5(10) = 110
Geeta got flats worth 90
So Geeta’s bank deposit = 110 - 90 = 20 lakhs
6th Answer: B. 90
7th Answer: 20 lakhs
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