At a management school, the oldest 10 dorms, numbered 1 to 10, need to be repaired urgently, The diagram represents the estimated repair costs (in Rs. Crores) for the 10 dorms. For any dorm, the estimated repair cost (in Rs. Crores) is an integer. Repairs with estimated cost Rs. 1 or 2 Crores are considered light repairs, repairs with estimated cost Rs. 3 or 4 are considered moderate repairs and repairs with estimated cost Rs. 5 or 6 Crores are considered extensive repairs. Further, the following are known: 1. Odd-numbered dorms do not need light repair; even-numbered dorms do not need moderate repair and dorms, whose numbers are divisible by 3, do not need extensive repair. 2. Dorms 4 to 9 all need different repair costs, with Dorm 7 needing the maximum and Dorm 8 needing the minimum
General Solution Let us go step-by-step. We have 10 dorms, each with some repairs needing to be done. Repair costs would be Rs. 1 crore, Rs. 2 crores, Rs. 3 crores, 4, 5 or 6 crores. From the irritating and unnecessary chart, we can infer that 2 dorms have repair costs of Rs. 1 crore each, 1 has a cost of Rs. 2c, 3 cost Rs. 3C, one each costs Rs. 4C and Rs, 5 C, and finally two dorms take up Rs. 6 crores each. Total cost should be Rs. 34 crores. Now, let us try to do this more visually. Even-numbered ones do not need moderate repairs – or all 4 moderate-repair dorms are odd-numbered. Likewise, all 3 light-repair ones are even-numbered. So, odd numbered dorms - 4 moderate and one extensive Even-numbered dorms - 3 light-repair ones and two extensive. Dorms 4 to 9 should have all costs from Rs. 1 crore to Rs. 6 crores. Dorm 7 should see Rs. 6 crores and dorm 8 should see Rs. 1 crore. Dorms 1, 3, 5, 9 should all have moderate numbers. So, three of them should cost RS. 3C and one should cost Rs. 4C. Dorms 4, 5, 6 and 9 should have costs 2, 3, 4, 5. Put these two together! Dorms 5 and 9 - Rs. 3C and Rs. 4C Dorms 4 and 6 - Rs. 2C and Rs. 5C. Dorms that are multiples of 3 do not need extensive repair. What does this tell us? So, dorm 6 should cost Rs. 2C and dorm 4 should cost Rs. 5C. What can we say about dorms 1 and 3? Both 1 and 3 should have seen moderate costs and since one of 5 or 9 costs Rs. 4C. Both 1 and 3 should cost Rs. 3C. What else do we have? Dorms 5 and 9 - Costs Rs. 3C and Rs. 4C in some order Dorms 2 and 10 - Costs Rs. 1C and Rs. 6C in some order. Now, let us go to the questions
3. Suppose further that: 1. 4 of the 10 dorms needing repair are women's dorms and need a total of Rs. 20 Crores for repair. 2. Only one of Dorms 1 to 5 is a women's dorm. What is the cost for repairing Dorm 9 (in Rs. Crores)? (TITA) Ans. 4 dorms should add up to Rs. 20 crores. Now, Rs. 20 crores is a large number. So, let us see if we can eliminate some possibilities from that. The top 3 costs are Rs. 6, 6 and 5. These 3 add up to Rs. 17. So, no women’s dorm can cost less than Rs. 3C. Now, only one of dorms from 1 to 5 is a women’s dorm. So, three out of 6 to 10 should be women’s dorms. What does this tell us? Dorms 6 and 8 see costs of Rs. 2C and 1C – these cannot be women’s dorms. So, 7, 9 and 10 should be women’s dorms. So, dorm 10 should cost Rs. 6C (as it cannot be Rs.1C) So, 7, 9 and 10 should be women’s dorms. Dorms 7 and 10 add up to a cost of Rs. 12 Crores. Dorm 9 and one other should add up to Rs. 8 crores. How much does dorm 9 cost? If dorm 9 were to cost Rs. 4C, then the one of dorms 1 to 5 should also cost Rs. 4C – this is impossible. So, dorm 9 should cost Rs. 3C. The Women’s dorms should be 7, 9, 10 and 4. Cost of repairing dorm 9 would be Rs. 3C.
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