Priority Sector Target: Two Constraints That Bind in Opposite Directions
A district-level branch must disburse ₹1.20 crore under priority sector in the current quarter, in two products. Kisan Credit Card (KCC) loans average ₹60,000 per farmer, and the branch can process at most 150 KCC files in the quarter. Self-help group (SHG) loans average ₹2,50,000 per group, and at most 25 SHG files can be processed. A separate board condition requires that SHG disbursement be at least 30% of the branch's total priority sector disbursement for the quarter, and the total must reach at least ₹1.20 crore. The branch head has already cleared 150 KCC files and asks you whether the target can be met without dropping any of them, and how many SHG groups would then be needed. A second question follows immediately: what is the smallest number of SHG groups that can satisfy both conditions at once, and how many KCC files may accompany it?
1. Keeping all 150 KCC files, can both the ₹1.20 crore target and the 30% SHG floor be satisfied? Show the arithmetic and state the disbursement that results.
Read the worked answer
150 KCC files × ₹60,000 = ₹90,00,000 = ₹90 lakh.
The shortfall to the ₹1.20 crore (₹120 lakh) target is ₹30 lakh, which is 12 SHG groups × ₹2,50,000. But 12 groups gives a share of 30/120 = 25%, below the 30% floor. Adding groups without dropping KCC files raises the total as well, so solve for s groups:
2.5s ≥ 0.30 × (90 + 2.5s) → 2.5s ≥ 27 + 0.75s → 1.75s ≥ 27 → s ≥ 15.43, so s = 16.
Check: KCC ₹90 lakh + SHG ₹40 lakh = ₹130 lakh, and 40/130 = 30.77%, which clears the floor. 16 groups is within the 25-file cap.
So yes, the target is achievable with all 150 KCC files - but only by overshooting to ₹1.30 crore, ₹10 lakh above the requirement. The 30% floor, not the ₹120 lakh target, is what forces the extra 10 SHG groups beyond the 12 that would otherwise suffice.
2. What is the minimum number of SHG groups that satisfies both conditions simultaneously, and what range of KCC files can accompany that minimum?
Read the worked answer
Let s = SHG groups at ₹2.5 lakh and k = KCC files at ₹0.6 lakh. The two conditions are 0.6k + 2.5s ≥ 120 and 2.5s ≥ 0.3(0.6k + 2.5s), which simplifies to s ≥ 0.10286k (equivalently k ≤ 9.72s).
Test s = 14: SHG = ₹35 lakh; the target needs k ≥ (120 − 35)/0.6 = 141.67, so k = 142; but the floor then needs 35 ≥ 0.3 × (85.2 + 35) = ₹36.06 lakh, which fails.
Test s = 15: SHG = ₹37.5 lakh; target needs k ≥ 82.5/0.6 = 137.5, so k ≥ 138; floor needs 37.5 ≥ 0.3(0.6k + 37.5) → k ≤ 145.8, so k ≤ 145.
Minimum is 15 SHG groups, with KCC files between 138 and 145 - e.g. 138 KCC (₹82.8 lakh) + 15 SHG (₹37.5 lakh) = ₹120.3 lakh, share 31.2%. Note the trap at k = 150: total ₹127.5 lakh but share only 29.4%, which fails. Adding KCC files dilutes the SHG share, so the upper limit on k is set by the floor, not by the 150-file capacity.
3. If the average KCC ticket falls to ₹55,000, how does the feasible plan change, and what operational risk should you flag to the branch head?
Read the worked answer
Redo with k at ₹0.55 lakh. The floor becomes 2.5s ≥ 0.3(0.55k + 2.5s) → 1.75s ≥ 0.165k → s ≥ 0.0943k.
Test s = 14: SHG ₹35 lakh; target needs k ≥ (120 − 35)/0.55 = 154.5, i.e. 155 files, above the 150-file capacity. Fails on capacity.
Test s = 15: SHG ₹37.5 lakh; target needs k ≥ 82.5/0.55 = 150 exactly. So 150 KCC (₹82.5 lakh) + 15 SHG (₹37.5 lakh) = ₹120.0 lakh, SHG share 31.25%, within the floor and within both caps.
The feasible plan is still 15 SHG groups, but it now sits exactly on two boundaries at once: the ₹120 lakh target is met with zero overshoot and the 150-file processing capacity is fully consumed. There is no buffer - one rejected KCC file or one SHG group dropping out breaks the target, and the branch has no spare capacity to replace either. That is the risk to flag: a plan that only works at 100% execution should be padded with extra SHG groups or an early start on file processing.