Question 11

A sum of money invested at simple interest becomes $$\frac{13}{10}$$ of itself in 2 years and 6 months. What is the rate (in percentage) of interest per annum?

Solution

Let sum of money invested = Rs. $$100x$$

=> Amount under simple interest = $$\frac{13}{10}\times100x=Rs.$$ $$130x$$

Thus, simple interest = $$130x-100x=Rs.$$ $$30x$$

Let rate of interest = $$r\%$$ and time period = 2.5 years

=> Simple interest = $$\frac{P\times R\times T}{100}$$

=> $$\frac{100x\times r\times2.5}{100}=30x$$

=> $$2.5r=30$$

=> $$r=\frac{30}{2.5}=12\%$$

=> Ans - (C)

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