In a taxi the fare for the first kilometre is (50) rupees and each next kilometre costs (15) rupees more. What is the total fare for (8) kilometres?

Correct answer: (820)

The direct answer is C: 820 rupees. Treat the fare charged for each kilometre as one term of an arithmetic progression. The first term is \\(a=50\\), the common difference is \\(d=15\\), and there are \\(n=8\\) terms. The eighth kilometre costs \\(a_8=50+7(15)=155\\). The total is the sum: \\(S_8=\\frac{8}{2}[2(50)+(8-1)(15)] =4(100+105)=4\\times205=820\\). Option A, 760, is too low and does not result from the correct eight-term sum. Option B, 790, is also an incorrect total, usually caused by using the wrong number of increases or an arithmetic error. Option C, 820, is correct because it adds the fares for kilometres 1 through 8. Option D, 850, is too high and may result from adding an extra increase. The important point is that the question asks for total fare, so finding only the eighth fare, 155, is not enough. Memory cue: first fare plus equal increase means AP; total means use the sum formula.