Question
The question consists of two
statements numbered "I and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Find the rate of interest per annum? Statement I: A sum of money becomes 5 times of itself in 20 years on simple interest. Statement II: An amount invested on simple interest becomes Rs. 4,500 in 6 years.Solution
ATQ,
Statement I: Let the principal be Rs. ‘P’ and the rate of interest be ‘R’% per annum. Simple Interest earned in 20 years = (P × R × 20) ÷ 100 = 0.20PR Total Amount after 20 years = 5P So, 5P – P = 0.20PR Or, 4P = 0.20PR Or, R = (4 ÷ 0.20) = 20% So, the rate of interest is 20% per annum. Hence, data in Statement I alone is sufficient. Statement II: Simple Interest for 6 years = (P × R × 6) ÷ 100 = 0.06PR Total Amount = P + 0.06PR = 4,500 So, P(1 + 0.06R) = 4,500 Here, we have two unknowns (P and R). Without more info, R cannot be determined. Hence, data in Statement II alone is not sufficient. Hence, Data in Statement I alone is sufficient, while Statement II alone is not sufficient.
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