A person has a certain sum with him. He invested 40% of total in bank at 10% simple interest and 25% of remaining to the charity. After 2 years he added 75% of remaining in the same bank account and remaining donated to the charity. If the difference between the total amount donated to the charity and total interest received from the bank account after 5 years is Rs 1550 then find the sum which the person has initially. एक व्यक्ति के पास एक निश्चित राशि होती है। उसने बैंक में कुल का 40% भाग 10% साधारण ब्याज पर और शेष 25% चैरिटी में निवेश किया। 2 वर्षों के बाद उसने उसी बैंक खाते में शेष 75% जोड़ा और शेष राशि दान में दे दी। यदि 5 वर्ष के बाद बैंक खाते से प्राप्त व्याज और दान के बीच कुल राशि का अंतर 1550 रुपये है तो उस राशि का पता लगाएं जो व्यक्ति के पास शुरू में थी |

Let initial sum = P. Bank investment: 40% of P = 0.4P at 10% SI for 5 years. Interest = 0.4P × 0.10 × 5 = 0.2P. After 2 years: remaining = 0.6P. 25% of remaining to charity = 0.25 × 0.6P = 0.15P. Remaining after charity = 0.45P. After 2 more years (total 4 years): 75% of remaining added to bank = 0.75 × 0.45P = 0.3375P. Total in bank after 4 years = 0.4P (initial) + 0.3375P = 0.7375P. This earns interest for 1 more year (year 5): 0.7375P × 0.10 × 1 = 0.07375P. Total interest = 0.07375P + interest on first 0.4P for 4 years = 0.07375P + 0.4P × 0.10 × 4 = 0.07375P + 0.16P = 0.23375P. Charity donations: 0.15P + remaining 25% of 0.45P = 0.15P + 0.1125P = 0.2625P. Difference: 0.2625P - 0.23375P = 0.02875P = 1550. So P = 1550/0.02875 ≈ 53913. This doesn't match option A (40000). Let me reconsider the timing. Actually re-reading: 'After 2 years he added 75% of remaining' - this means at year 2, not year 4. Let me redo: Bank: 0.4P from year 0 to year 5 = 0.4P × 0.10 × 5 = 0.2P. After 2 years: charity = 0.15P, remaining = 0.45P. 75% of 0.45P = 0.3375P added to bank at year 2. This 0.3375P earns interest for 3 years: 0.3375P × 0.10 × 3 = 0.10125P. Total interest = 0.2P + 0.10125P = 0.30125P. Total charity = 0.15P + 0.25 × 0.45P = 0.15P + 0.1125P = 0.2625P. Difference: 0.30125P - 0.2625P = 0.03875P = 1550. P = 1550/0.03875 = 40000. This matches option A.