Arithmetic Progression Word Problem

Monthly earnings that rise by a fixed increment form an arithmetic progression, and the cumulative total is its sum, a typical JEE Advanced application. Here a = 200, d = 25, and two years comprise n = 24 months. The sum is S_24 = (24/2)[2(200) + (24 - 1)(25)] = 12[400 + 575] = 12 × 975 = 11700 rupees. Option 10800 ignores the increment and simply multiplies 200 by 54, an inconsistent count. Option 12000 rounds away the arithmetic structure. Option 9600 multiplies 200 by 24 without any increment, giving only the base pay. Hence the total is 11700 rupees. The lesson is that any real-world quantity increasing by equal steps per period is modelled by an AP, so cumulative totals are computed with the sum formula rather than by tedious term-by-term addition, a modelling skill JEE Advanced frequently disguises in word problems. Plausibility check: the last month's pay is 200 + 23·25 = 775, and the average of first and last months is (200 + 775)/2 = 487.5, so 487.5 × 24 = 11700, confirming the sum through the average-term method.