Multiple choice

A man invested a sum at the rate of 20% per annum compounded annually and after two years he reinvested the half of the initial amount. The man got Rs. 1080 as interest after three years, find the amount received by him if he invested the same sum at 10% per annum on simple interest for 2 years? एक व्यक्ति ने एक राशि को 20% वार्षिक चक्रवृद्धि की दर से निवेश किया और दो वर्ष बाद उसने प्रारंभिक राशि का आधा पुनर्निवेश किया। आदमी को 1080 रु 3 वर्ष के बाद ब्याज के रूप में, प्राप्त हुआ उसके द्वारा प्राप्त राशि ज्ञात कीजिए यदि वह समान राशि को 10% प्रति वर्ष की दर से साधारण ब्याज पर 2 वर्ष के लिए निवेश करता है?

  1. Rs. 2400 रु. 2400

  2. Rs. 2450 रु. 2450

  3. Rs. 2750 रु. 2750

  4. Rs. 2600 रु. 2600

  5. None of these इनमें से कोई नहीं
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A Correct answer
Explanation

Let initial sum = P. After 2 years at 20% compound interest: amount = P(1.2)² = 1.44P. Half of initial amount (P/2) is reinvested for 1 more year at 20%: interest = P/2 × 0.2 × 1 = 0.1P. Total interest after 3 years = (1.44P - P) + 0.1P = 0.44P + 0.1P = 0.54P = 1080. So P = 1080/0.54 = 2000. Simple interest at 10% for 2 years: SI = 2000 × 0.1 × 2 = 400. Total amount = 2000 + 400 = 2400. Options B (2450), C (2750), and D (2600) are incorrect amounts.

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