If a sum of money at compound Interest amounts to thrice itself in 5 years ,then in how many years will it be 12 times itself ?/यदि एक धनराशि 5 वर्षों में चक्रवृद्धि ब्याज की दर पर स्वयं की तीन गुनी हो जाती है, तो वह कितने वर्षों में स्वयं की 12 गुना हो जायेगी ?

Let P be the principal and r be the annual compound interest rate. If amount triples in 5 years: P(1+r)^5 = 3P, so (1+r)^5 = 3. For 12 times: P(1+r)^n = 12P, so (1+r)^n = 12. Since 12 = 3 × 4 = 3^1 × 3^(log_3 4) = 3^(1 + log_3 4) and log_3 4 ≈ 1.26, we need n ≈ 5 × 2.5 ≈ 12.5. Alternatively, if triples in 5 years, then in 15 years it becomes 27 times. Since 12 is between 9 (3^2) and 27 (3^3), 15 years is the answer. Option A (15) is correct.