Maths · Arithmetic and Geometric progressions
A man saved RS. 200 in each of the first three months of his service. In each of
A man saved RS. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after.
- A. 18 months
- B. 19 months
- C. 20 months
- D. 21 months
Step-by-step solution
Savings: first 3 months: Rs. 200 each. From month 4 onward: arithmetic progression with first term 240, common difference 40. Let additional months be k. Total savings = 600 + sum of AP for k terms = 600 + (k/2)(2*240 + (k-1)*40) = 20k^2 + 220k + 600. Set equal to 11040: 20k^2 + 220k + 600 = 11040 → divide 20: k^2 + 11k + 30 = 552 → k^2 + 11k - 522 = 0. Discriminant = 121 + 2088 = 2209, sqrt=47. Positive root: k = 18. Total months = 3 + 18 = 21.
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