If the coefficient of variation of the rainfall values of the existing rain-gauge stations is 30 and the desired error in the basin-mean rainfall estimate is 10%, the optimum number of rain-gauge stations is

The optimum number of rain-gauge stations N = (Cv/p)², where Cv is the coefficient of variation of rainfall values at existing stations (%) and p is the desired percentage error in the mean rainfall estimate. N = (30/10)² = 3² = 9. This formula (from IS 4987) ensures the gauge network provides a mean areal rainfall estimate within ±10% of the true value. If the existing number of gauges is less than N, additional gauges must be added to meet the accuracy requirement.

ScoreCardAI links this solution with subject, topic and difficulty signals so your scorecard can identify weak areas after a full mock test.