Q.1.The difference in simple interest and compound interest on a certain sum of money in 2 years at 10 % p.a. is Rs. 50. The sum is
a) Rs. 10000
b) Rs. 6000
c) Rs. 5000
d) Rs. 2000
e) None of these
Q.2. The difference in simple interest and compound interest on a certain sum of money in 2 years at 18 % p.a. is Rs. 162. The sum is
a) Rs. 4000
b) Rs. 5200
c) Rs. 4250
d) Rs. 5000
e) None of these
Q.3. The compound interest on a certain sum of money for 2 years is Rs. 208 and the simple interest for the same time at the same rate is Rs. 200. Find the rate %.
a) 5 %
b) 6 %
c) 7 %
d) 4 %
e) 8 %
Q.4.The difference between compound interest and simple interest on a certain sum for 2 years at 10 % is Rs. 25. The sum is
a) Rs. 1200
b) Rs. 2500
c) Rs. 750
d) Rs. 1250
e) Rs. 2000
Q.5.The simple interest on a certain sum for 3 years in Rs. 225 and the compound interest on the same sum for 2 years is Rs. 165. Find the rate percent per annum.
a) 20 %
b) 2.5 %
c) 5 %
d) 15 %
e) 7.5%
Q.6.The simple interest on a sum of money for 2 years is Rs. 150 and the compound interest on the same sum at same rate for 2 years is Rs. 155. The rate % p.a. is
a) 16 %
b) 20/3 %
c) 12 %
d) 10 %
e) None of these
Q7.Mihir’s capital is 5/4 times more than Tulsi’s capital. Tulsi invested her capital at 50 % per annum for 3 years (compounded annually). At what rate % p.a. simple interest should Mihir invest his capital so that after 3 years, they both have the same amount of capital?
a) 20/3 %
b) 10 %
c) 50/3 %
d) 1.728 %
e) None of these
Q8.The difference in simple interest and compound interest on a certain sum of money in 3 years at 10 % p.a. is Rs. 372. The sum is
a) Rs. 8000
b) Rs.9000
c) Rs. 10000
d) Rs. 12000
e) None of these
Q9.Sahil’s capital is 1/6 times more than Chaya’s capital. Chaya invested her capital at 20 % per annum for 2 years (compounded annually). At what rate % p.a. simple interest should Sahil invest his capital so that after 2 years, they both have the same amount of capital?
a) 10%
b) 11 5/7%
c) 20%
d) 13 5/7%
e) None of these
Q10.The difference in simple interest and compound interest on a certain sum of money in 3 years at 20 % p.a. is Rs. 640. The sum is
a) Rs. 5000
b) Rs. 8500
c) Rs. 8250
d) Rs. 6000
e) None of these
On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to Rs. 63 ?
A. Rs. 24600
B. Rs. 24800
C. Rs. 25200
D. Rs. 25500
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{Rate of interest = 5}}\% {\text{ per annum}} \cr & {\text{Time = 2 year}} \cr & {\text{Accroding to question,}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{r}{{100}}} \right)}^n} - 1} \right] - \frac{{P \times r \times t}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{P \times 5 \times 2}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {\frac{{105}}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left( {\frac{{11025 - 10000}}{{10000}}} \right) - \frac{{10P}}{{100}} = 63 \cr & \Rightarrow \frac{{1025P}}{{10000}} - \frac{{10P}}{{100}} = 63 \cr & \Rightarrow \frac{{1025P - 1000P}}{{10000}} = 63 \cr & \Rightarrow 25P = Rs.630000 \cr & \Rightarrow P = \frac{{630000}}{{25}} \cr & \Rightarrow P = Rs. 25200 \cr & {\text{Hence}},\,{\text{sum Rs}}{\text{. 25200}} \cr} $$
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Question
On what sum of money will the difference between the compound interest and simple interest for 2years be equal to Rs 25 if the rate of interest charged for both is 5% p.a.
Hint:
Use the formula of compound interest and simple interest to get the principal amount.
The correct answer is: Rs 10000
Complete step by step solution:
Let the principal amount = P
It is given that the rate of interest R = 5% and number of years T = 2 years.
So, compound interest for 2 years =
Simple interest
for 2 years =
It is given that compound interest - simple interest = 25 Rupees
That is, Rupees.
Hence the principal amount = Rs 10000
Hence the principal amount = Rs 10000