Scheduling Six KCC Enhancement Files in a Branch
Six applications for enhancement of Kisan Credit Card limits - P, Q, R, S, T and U - must be disposed of by a cooperative bank's agriculture desk, one on each working day from Monday to Saturday. The branch's scheduling rules are: R must be taken up exactly two days after P; S is fixed for Wednesday because the land-record officer visits only that day; T cannot be placed on Monday or on Saturday; U must be taken up on the day immediately before Q; and Q cannot be placed on Saturday. The amounts sought are P ₹2.50 lakh, Q ₹1.20 lakh, R ₹3.00 lakh, S ₹0.80 lakh, T ₹4.20 lakh and U ₹1.60 lakh. Under the bank's delegation, an enhancement above ₹1.60 lakh needs mortgage of land, while one at or below ₹1.60 lakh is collateral-free. The branch has one empanelled valuer who can attend only on a day when a mortgage file is taken up.
1. Work out the day on which each application must be taken up, showing how you eliminate the arrangements that fail.
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Fix the two positions the rules pin down, then test the rest.
- S occupies Wednesday, that is slot 3.
- R is exactly two days after P, so the only surviving pairs are (P on Tuesday, R on Thursday) and (P on Thursday, R on Saturday). P on Monday or Wednesday collides with S, and P on Friday would push R beyond Saturday.
- Test P on Tuesday, R on Thursday: the free slots are Monday, Friday and Saturday. U and Q must be consecutive, and the only consecutive pair available is Friday and Saturday, forcing T into Monday - which the T condition forbids. Rejected.
- Test P on Thursday, R on Saturday: free slots are Monday, Tuesday and Friday. The only consecutive pair is Monday and Tuesday, so U is Monday, Q is Tuesday and T takes Friday, which is neither Monday nor Saturday. Accepted.
Final order: Monday U, Tuesday Q, Wednesday S, Thursday P, Friday T, Saturday R. The arrangement is unique. A candidate who gets T on Monday has mishandled the T condition, not the P–R condition.
2. On which days must a mortgage be executed, and what is the total amount of collateral-backed exposure the branch is creating that week?
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Compare each amount with the ₹1.60 lakh threshold, remembering that the rule says above ₹1.60 lakh.
- P, ₹2.50 lakh, Thursday - mortgage needed.
- Q, ₹1.20 lakh, Tuesday - collateral-free.
- S, ₹0.80 lakh, Wednesday - collateral-free.
- T, ₹4.20 lakh, Friday - mortgage needed.
- R, ₹3.00 lakh, Saturday - mortgage needed.
- U, exactly ₹1.60 lakh, Monday - collateral-free, because the delegation catches only amounts above the threshold; equality falls on the customer's side of the line.
So the valuer is required on Thursday, Friday and Saturday, and the mortgage-backed exposure created that week is ₹2.50 + ₹4.20 + ₹3.00 = ₹9.70 lakh. Note the operational consequence: the valuer must be booked for three consecutive days, and U on Monday, being at the threshold, is the file most likely to be wrongly held up by a clerk reading the rule loosely.
3. The manager learns that T's applicant will be out of station on Friday. Nothing else may be changed without written approval. What do you advise?
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Under the stated rules there is no valid schedule at all, so a rule must be relaxed - and the cheapest one to relax is S's Wednesday fixation.
Reasoning: in the unique solution T necessarily falls on Friday, so removing Friday leaves zero arrangements that satisfy all five conditions simultaneously. This is not a matter of reshuffling; it is infeasibility, and the answer must say so rather than invent a schedule.
Two routes, in order of practicality:
- Ask the land-record officer to come on Friday instead of Wednesday. Then S takes Friday and the order becomes: Monday U, Tuesday Q, Wednesday T, Thursday P, Friday S, Saturday R. Check: R is two days after P; T is on Wednesday; U immediately precedes Q; Q is not on Saturday. All conditions hold.
- If the officer cannot move, the next softest rule is U-immediately-before-Q, but that weakens the sequencing control the branch actually cares about.
File the approval for the change in writing before the week begins - a verbal rearrangement is exactly the audit observation the branch wants to avoid.