Allocating Hand Pumps and Toilets from a Block Survey
A block development office in Bihar compiled a baseline survey of four panchayats before sanctioning drinking-water and sanitation works. The recorded figures are:
| Panchayat | Population | Households | Hand pumps | Household toilets | Literate persons |
|---|---|---|---|---|---|
| A | 4200 | 700 | 14 | 350 | 2730 |
| B | 3150 | 630 | 10 | 441 | 2205 |
| C | 5600 | 800 | 18 | 480 | 3360 |
| D | 2450 | 490 | 6 | 294 | 1470 |
The district officer will release funds for 20 new hand pumps to the panchayat that is worst served, and will keep releasing pumps until that panchayat reaches the block average of persons per hand pump. A separate sanitation grant is to go to the panchayat with the lowest share of households having toilets, provided the scheme brings that share up to 70%.
1. Which panchayat is worst served in terms of hand pumps? Support your answer with figures and explain why counting pumps alone misleads.
Read the worked answer
Persons per hand pump:
- A: 4200/14 = 300
- B: 3150/10 = 315
- C: 5600/18 = 311.1
- D: 2450/6 = 408.3
D is worst served, at about 408 persons per pump against A's 300 - roughly 36% worse than the best-served panchayat.
Counting pumps alone misleads badly. C has the most pumps (18) yet is only third best, because it also has the largest population; B has fewer pumps than A yet sits between A and C in the ranking. The number of pumps says nothing without the population it serves, so the defensible indicator is persons per pump, and D gets the sanction.
2. Using the block average, work out how many pumps D actually needs to reach it. What should be done with the remaining pumps of the 20?
Read the worked answer
Block totals: population = 4200 + 3150 + 5600 + 2450 = 15 400; pumps = 14 + 10 + 18 + 6 = 48.
Block average = 15 400/48 = 320.8 persons per pump.
Pumps D needs to reach that figure = 2450/320.8 = 7.64, rounded up to 8 pumps (7 gives 350 persons per pump, still above average; 8 gives 306, just below). D already has 6, so it needs 2 more pumps, not 20.
Pushing all 20 into D would leave it with 26 pumps, about 94 persons per pump - less than a third of the block average - and would waste the grant. The remaining 18 should go to the next-worst panchayats (B at 315 and C at 311), after recalculating the average, or be held against a fresh survey rather than being forced into one village.
3. Which panchayat should receive the sanitation grant and how many more toilets does it need? Is the literacy column relevant?
Read the worked answer
Share of households with toilets:
- A: 350/700 = 50%
- B: 441/630 = 70%
- C: 480/800 = 60%
- D: 294/490 = 60%
A is lowest at 50%, so A qualifies for the grant. To reach 70%, A needs 0.70 × 700 = 490 toilets, that is 490 − 350 = 140 more toilets.
The literacy column is a distractor. A's literacy rate is 2730/4200 = 65%, which is not the lowest - C and D are both at 60% and B is highest at 70%. The condition attached to the grant concerns toilet coverage only, so literacy does not change the answer; using it would send the money to the wrong panchayat.