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Questions 1-3: A dealer deals only in colour TVs and VCRs. He wants to spend up to Rs.12 lakhs to buy 100 pieces. He can purchase a colour TV at Rs.10,000 and a VCR at Rs.15,000. He can sell a colour TV at Rs.12,000 and a VCR at Rs.17,500. His objective is to maximize profits. Assume that he can sell all the items that he stocks.

1. For the maximum profit, the number of colour TVs and VCRs that he should respectively stock are

• (a) 80, 20
• (b) 20, 80
• (c) 60, 40
• (d) None of these

2. If the dealer would have managed to get an additional space to stock 20 more items, then for maximizing profit, the ratio of number of VCRs and number of TVs that he should stock is

• (a) 7 : 3
• (b) 0
• (c) 1 : 2
• (d) None of these

3. The maximum profit, in rupees lakh, the dealer can earn from his original stock if he can sell a colour TV at Rs. 12200 and VCR at Rs.18300 is

• (a) 2.64
• (b) 2.49
• (c) 2.72
• (d) 2.87

Questions 4-6: Ghosh Babu has a certain amount of property consisting of cash, gold coins and silver bars. The cost of a gold coin is Rs. 4000 and the cost of a silver bar is Rs. 1000. Ghosh Babu distributed his property among his daughters equally. He gave to his eldest daughter gold coins worth 20% of the total property and Rs. 25000 in cash. The second daughter was given silver bars worth 20% of the remaining property and Rs. 50000 cash. He then gave each of the third and fourth daughters equal number of gold coins and silver bars both together accounting each for 20% of the property remaining after the previous distribution and Rs. 25000 more than what the second daughter had received in cash.

4. The amount of property in gold and silver possessed by Ghosh Babu is

• (a) 2,25,000
• (b) 2,75,000
• (c) Rs. 4,25,000
• (d) None of these

5. Total property of Ghosh Babu (in Rs.lakh) is

• (a) 5.0
• (b) 7.5
• (c) 10.0
• (d) 12.5

6. If Ghosh Babu had equal number of gold and silver bars, the number of silver bars he has is

• (a) 90
• (b) 60
• (c) 75
• (d) 55

7. A car after traveling 18 km from a point A developed some problem in the engine and speed became 4/5 of its original speed. As a result, the car reached point B, 45 minutes late. If the engine had developed the same problem after traveling 30 km from A, then it would have reached B only 36 minutes late. The original speed of the car (in km per hour) and the distance between the points A and B (in km) is

• (a) 25, 130
• (b) 30,150
• (c) 20, 90
• (d) None of these

8. A, B and C individually can finish a work in 6, 8 and 15 hours respectively. They started the work together and after completing the work got Rs.94.60 in all. When they divide the money among themselves, A, B and C will respectively get (in Rs.)

• (a) 44, 33, 17.60
• (b) 43, 27.20, 24.40
• (c) 45, 30, 19.60
• (d) 42, 28, 24.60

9. Two trains are traveling in opposite direction at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had traveled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in metres)?

• (a) 112, 78.40
• (b) 97.78, 55
• (c) 102.78, 50
• (d) 102.78, 55

10. N the set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is

• (a) 61250
• (b) 65525
• (c) 42455
• (d) 62525

(Above questions were asked in CAT 1990 Paper)