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  • Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?

Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?

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\text{As per the question, she saves 32 in the first month, 36 in the second, and so on.} \\ \text{Sequence: } 32, 36, 40, \ldots \\ \text{Here, first term }(a) = 32 \\ \text{Common difference }(d) = 36 - 32 = 4 \\ \text{Let in } n \text{ month she saves Rs. 2000} \\ S_{n} = \frac{n}{2}\left[2a + (n-1)d\right] \\ 2000 = \frac{n}{2}[2 \times 32 + (n-1) \times 4] \\ 4000 = n[64 + 4n - 4] \\ 4000 = n[60 + 4n] \\ 4n^2 + 60n - 4000 = 0 \\ \text{Divide by 4:} \\ n^2 + 15n - 1000 = 0 \\ n^2 + 40n - 25n - 1000 = 0 \\ n(n + 40) - 25(n + 40) = 0 \\ (n + 40)(n - 25) = 0 \\ n = -40 \text{ (months cannot be negative, which is not possible)}, n = +25 \\ \text{Hence, it takes 25 months to save Rs. 2000.}

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