Quantity I. A= p [1+`R/100` ]t ⇒ 3P = P [1+`R/100` ]4 ⇒ 3 = [1+ `R/100` ]4 …………(i) A= p [1+`R/100` ]t ⇒ 9P = P [1+`R/100` ]t ⇒ 32 = [1+ `R/100` ]t …………….(ii) From (i) and (ii) [1+`R/100` ]4 × 2 = [1+`R/100` ]t t = 8 years Quantity II. Since the amount was Rs 100. It becomes Rs 300 in 20 years. Rs 300 – Rs 100 = Rs 200 interest In 20 years, interest is Rs 200 In 1 year, the interest is Rs`200/20` Rate of interest = 10% per annum. = 100 x 50 / 100 x 10 = 5 years Hence Quantity I > Quantity II
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