Question: Suppose further that:
4 of the 10 dorms needing repair are women’s dorms and need a total of Rs. 20 Crores for repair.
Only one of Dorms 1 to 5 is a women’s dorm.
What is the cost for repairing Dorm 9 (in Rs. Crores)?
Explanation:
Let us tabulate the information given in the bar chart. As per condition (i) we get the following information
From this we can conclude that Dorm 6 would require light repairs and that Dorm 3 and 9 would require moderate repairs. Now following condition (2), we get to know that Dorm 7 would require 6 cr for repair. and Dorm 8 would required 1 cr. This means that in light repairs, Dorm 8 requires 1 crore for repair and Dorm 2 requires 6 crores for repair. Now as each of Dorms to 9 requires a different amount for repairs, and no even numbered dorm requires ,moderate repair, it would imply that Dorm no 4 requires heavy repairs. Already Dorm 7 needs the maximum amount for repairs, (i.e, 6 crores) which means that Dorm4 would require 5 crores for repair. Now Dorm 9 would require 3 or 4 cr for repair. This leads us to 2 possible cases.
In case 1, as 4 cr is required for Dorm no 9, 3 cr will be required for Dorm no. 5. Also, as no even numbered dorm can have a moderate expenditure, out of the remaining 4 dorms, 1 and 3 (which are also the only odd numbered dorms out of the remaining 4 dorms) will have an expenditure of 3 crores (also since there is only 1 dorm which has a expense of 4 cr which in this case is the expense for Dorm 9). This leaves out only Dorm 2 and Dorm 10, one of these 2 dorms will have an expense of 1 cr and the other an expense of 6 crores.
Now the only way the cost of repairing 4 dorms adds upto 20 crores is when the repair cost of 2 of the dorms is 6 crores each, the repair cost of the 3rd dorm is 5 crores and the repair cost of the 4th dorm is 3 crores.
This means that dorms 7 and 4 are definitely women’s dorms. Now if we follow condition. Now if we follow condition (2), we get to know that from Dorm 1 to 5 only Dorm 4 is a women’s dorm. So, the remaining 3 women’s dorms have to be from Dorm 6 to 10. Now from Dorm 6 to Dorm 10, we already know that Dorm 7 is a women’s dorm. Now the Dorm for which the cost of repair is 3 crore has to be a dorm where number is between 6 to 10. This only happens in case 2, where Dorm 9 is one of the 3 dorm that costs Rs. 3 crore to repair. Also in case 2, the second dorm that cost Rs.6 crores to repair has to be Dorm No. 10 to satisfy condition (2).
Hence the 4 women’s dorms that Rs.20 crores to repair are Dorms 7, 10, 4 and 9. So the cost of repairing Dorm 9 is Rs. 3 crores.
Answer: 3