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AFCAT Model Paper 7

Question : 38 of 100

Marks: +1, -0

Solution:

Given:

The simple interest on a sum of money for one year is Rs. 260 and

The compound interest on the same sum for two years is Rs. 540.80

Formula Used:

SI = \frac{P \times r \times t}{100}

CI = P\left(\left(1+\frac{r}{100}\right)^{t} - 1\right)

Where p is the sum, r is rate and t is the time in years.

Calculation:

According to the question

⇒

260 = \frac{p \times r}{100}

⇒

540.80 = p\left(\left(1+\frac{r}{100}\right)^{2} - 1\right)

Dividing the two equations we get,

⇒

\frac{260}{540.80} = \frac{\frac{r}{100}}{\left(1+\frac{r}{100}\right)^{2} - 1}

⇒

\frac{25}{52} = \frac{\frac{r}{100}}{\left(\frac{r}{100}\right)^{2} + \frac{2r}{100}}

⇒

\frac{1}{100} + 2 = \frac{52}{25}

\Rightarrow r = \frac{200}{25}

∴ The rate percent per annum is 8.

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