A course fee is 250 rupees in the first month and increases by 75 rupees each next month. In which month will the fee be 1075 rupees?

Correct answer: 12

The governing concept is the nth term of an arithmetic progression, because the fee increases by the same amount, ₹75, every month. The first term is a = 250 and the common difference is d = 75. For the fee in the nth month, use a_n = a + (n − 1)d. Substituting the required fee gives 1075 = 250 + 75(n − 1). Therefore, 825 = 75(n − 1), so n − 1 = 11 and n = 12. Hence the fee becomes ₹1075 in the twelfth month, making option B correct. The sum formula is not needed because the question asks for the fee in one particular month, not the total fee collected over several months. The other options would correspond to using an incorrect number of monthly increases.