Choosing between two wards for a ₹3 lakh water connection grant
A Gram Panchayat's household survey covers six wards. Households: W1 240, W2 190, W3 300, W4 160, W5 220, W6 90. Households with a functional piped water connection: W1 168, W2 133, W3 270, W4 80, W5 130, W6 63. A grant of ₹3.00 lakh is available for new connections. The engineering estimate is ₹4,500 per connection in W4, where houses are scattered on a hill slope, and ₹2,800 per connection in W5, which is compact. At the Grama Sabha the W4 member argues that his ward has the lowest coverage and must come first; the W5 member replies that her ward has more households without water. Both claims are arithmetically correct.
1. Compute the Gram Panchayat's overall coverage, and each ward's coverage and number of unserved households. Which ward is worst, and by which measure?
Read the worked answer
Totals: households = 240+190+300+160+220+90 = 1,200. Connections = 168+133+270+80+130+63 = 844. Overall coverage = 844 ÷ 1,200 = 70.3%; unserved = 356.
| Ward | Households | Connected | Coverage | Unserved |
|---|---|---|---|---|
| W1 | 240 | 168 | 70.0% | 72 |
| W2 | 190 | 133 | 70.0% | 57 |
| W3 | 300 | 270 | 90.0% | 30 |
| W4 | 160 | 80 | 50.0% | 80 |
| W5 | 220 | 130 | 59.1% | 90 |
| W6 | 90 | 63 | 70.0% | 27 |
Answer: W4 is worst on the percentage measure (50.0%, twenty points below the GP average). W5 is worst on the absolute measure (90 unserved households, the largest single block of deprived households). The two members are measuring different things, which is why the debate cannot be settled by assertion.
2. Give two defensible allocation options for the ₹3.00 lakh with full arithmetic, and state which you would recommend and why.
Read the worked answer
Option A - maximise households served (efficiency). Fund W5 fully: 90 × ₹2,800 = ₹2,52,000. Balance ₹48,000 funds 48,000 ÷ 4,500 = 10.67, i.e. 10 connections in W4 = ₹45,000, leaving ₹3,000. Households served = 100; unserved falls to 256.
Option B - worst-first equity. W4 alone cannot be completed: 80 × ₹4,500 = ₹3.60 lakh, which is ₹60,000 short. ₹3.00 lakh buys 3,00,000 ÷ 4,500 = 66 connections, leaving 14 households, and completion needs a committed ₹63,000 in the next instalment.
Option C - proportional. Split in the ratio of unserved households, 90 : 80, giving roughly ₹1.58 lakh to W5 (56 connections) and ₹1.42 lakh to W4 (31 connections): 87 households.
Recommendation: Option A, provided the Grama Sabha records a written commitment that W4 is first in the next instalment. It serves the most households per rupee and avoids part-built networks. It is defensible only because the equity gap is acknowledged and scheduled; without that commitment it becomes a choice for the compact ward over the hill ward and will not survive a social audit.
3. A member suggests counting W6's 18 metered but non-functional connections as 'covered' to lift the Panchayat's overall figure above 72%. Respond.
Read the worked answer
Reject it. Coverage in a rural water programme is measured by functional household tap connections - a connection that actually delivers water for the prescribed hours and quality - not by the existence of a meter or a pipe. A metered connection with no supply is a defunct asset, and counting it:
- misstates the baseline, so the ward looks served and the repair never enters the plan;
- corrupts the data uploaded to the monitoring portal, which is a data-integrity issue and can attract an audit para and withholding of funds;
- shifts the burden to the households, usually women, who continue to fetch water.
The correct entries are: W6 connected and functional 63 (70.0%), 18 non-functional to be shown separately with the reason (source failure, pump repair, pipeline damage) and costed for repair. If the Panchayat wants a better number, it should repair the 18 - the arithmetic improves only when the water flows.