Question : The difference between compound interest and simple interest for 3 years and 2 years are in the ratio 23 : 7, respectively. What is the rate of interest per year (in %)?
Option 1: $\frac{200}{7}$
Option 2: $\frac{100}{7}$
Option 3: $\frac{300}{7}$
Option 4: $\frac{400}{7}$
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Correct Answer: $\frac{200}{7}$
Solution : Difference between CI and SI for 2 years = $\frac{PR^2}{10000}$ Difference between CI and SI for 3 years = $\frac{PR^2}{10000}×\frac{300+R}{100}$ Ratio = $\frac{PR^2}{10000}×\frac{300+R}{100}$:$\frac{PR^2}{10000}$ ⇒ $23 : 7 = \frac{300+R}{100}:1$ ⇒ $\frac{300+R}{100} = \frac{23}{7}$ ⇒ $7(300+R) = 2300$ ⇒ $ R = \frac{200}{7}$% Hence, the correct answer is $\frac{200}{7}$.
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Question : A certain sum was invested at the rate of 10% for 2 years at Compound interest and compounded annually. The same sum was invested for the same period and the same rate of interest at Simple interest. If the difference between Compound interest and Simple interest was Rs. 200 find the sum.
Option 1: Rs. 30,000
Option 2: Rs. 25,000
Option 3: Rs. 22,000
Option 4: Rs. 20,000
Question : If INR 2,000 is invested at a simple interest rate of 5% per annum and the interest is added to the principal after 10 years, then in how many years will it amount to INR 4,000 at the same rate of interest?
Option 1: $18 \frac{2}{3}$ years
Option 2: $16 \frac{1}{3}$ years
Option 3: $16 \frac{2}{3}$ years
Option 4: $18 \frac{1}{3}$ years
Question : The Simple interest and Compound interest that can be earned in two years at the same rate are Rs. 1,000 and Rs. 1,040, respectively. What is the rate (percent per annum) of interest?
Option 1: 9
Option 2: 10
Option 3: 8
Option 4: 11
Question : The simple interest on a sum of money is $\frac {1}{16}$th of the principal and the number of years is equal to the rate per cent per annum. The rate per annum is:
Option 1: $1\frac{1}{2}$%
Option 2: $2\frac{1}{2}$%
Option 3: $3\frac{1}{2}$%
Option 4: $4\frac{1}{2}$%
Question : If the difference between the compound interest and simple interest on a certain sum of money for 3 years at the rate of 4% per annum is INR 76, then what is the sum?
Option 1: INR 16,725
Option 2: INR 12,925
Option 3: INR 15,625
Option 4: INR 18,825
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