Multiple choice

A certain sum in certain time becomes Rs.500 at the rate of 8% per annum simple interest and the same sum amounts to Rs.200 at the rate of 2% simple interest in the same duration. Find the time. एक निश्चित धनराशि निश्चित समय में 8% प्रति वर्ष साधारण ब्याज की दर पर 500 रू.हो जाती है और यही धनराशि 2% प्रतिवर्ष साधारण ब्याज की दर पर इसी समय में 200 रू. हो जाती है। समय ज्ञात कीजिए।

  1. 25 years/वर्ष

  2. 30 years/वर्ष

  3. 40 years/वर्ष

  4. 50 years/वर्ष

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D Correct answer
Explanation

For simple interest: Amount = Principal + (Principal × Rate × Time)/100. Let P be principal and T be time. At 8%: 500 = P + (P × 8 × T)/100 = P(1 + 0.08T). At 2%: 200 = P(1 + 0.02T). Dividing the equations gives 500/200 = (1 + 0.08T)/(1 + 0.02T). Solving: 2.5(1 + 0.02T) = 1 + 0.08T, which gives 2.5 + 0.05T = 1 + 0.08T, so 1.5 = 0.03T, and T = 50 years.