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Question Detail
Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is
- Rs 1650
- Rs 1750
- Rs 1850
- Rs 1950
Answer: Option B
Explanation:
\begin{aligned}
C.I. = (4000 \times(1+\frac{10}{100})^2 - 4000) \\
= 4000 * \frac{11}{10} * \frac{11}{10} - 4000 \\
= 840 \\
\text{So S.I. = } \frac{840}{2} = 420\\
\text{So Sum = } \frac{S.I. * 100}{R*T} \\
= \frac{420 * 100}{3*8} \\
= Rs 1750
\end{aligned}
1. We need to divide Total Sum Rs. 3364 between Ram and Sham so that Ram's share at the end of 5 years may equal to Sham's share at the end of seven years with compound interest rate at 5 percent.
- 1864 and 1500
- 1764 and 1600
- 1664 and 1700
- 1564 and 1800
Answer: Option B
Explanation:
It is clear from question that Ram's share after five years = Sham's share after seven years
Hence we can conclude following :
\begin{aligned}
\text{(Rams's present share)}\left(1 + \dfrac{5}{100}\right)^5 = \text{(Sham's present share)}\left(1 + \dfrac{5}{100}\right)^7\\
=> \dfrac{\text{(Ram's present share)}}{\text{(Sham's present share)}}= \dfrac{\left(1 + \dfrac{5}{100}\right)^7}{\left(1 + \dfrac{5}{100}\right)^5} \\ = \left(1 + \dfrac{5}{100}\right)^{(7-5)} = \left(1 + \dfrac{5}{100}\right)^2 \\ = \left(\dfrac{21}{20}\right)^2 = \dfrac{441}{400}
\end{aligned}
Ram's present share : B's present share = 441 : 400
\begin{aligned}
\text{As amount is Rs.3364, Ram's share = }3364 \times \dfrac{441}{(441+400)} \\\\
= 3364 \times \dfrac{441}{841} = 4 \times 441 = \text{ Rs. 1764}
\end{aligned}
So Sham's share is = 3364-1764 = 1600
2. Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quarterly
- Rs 2520
- Rs 2521
- Rs 2522
- Rs 2523
Answer: Option C
Explanation:
Please remember, when we have to calculate C.I. quarterly then we apply following formula if n is the number of years
\begin{aligned}
Amount = P(1+\frac{\frac{R}{4}}{100})^{4n}
\end{aligned}
Principal = Rs.16,000;
Time=9 months = 3 quarters;
Rate = 20%, it will be 20/4 = 5%
So lets solve this question now,
\begin{aligned}
Amount = 16000(1+\frac{5}{100})^3 \\
= 18522\\
C.I = 18522 - 16000 = 2522
\end{aligned}
3. What will be the difference between simple and compound interest @ 10% per annum on the sum of Rs 1000 after 4 years
- Rs 62.10
- Rs 63.10
- Rs 64.10
- Rs 65.10
Answer: Option C
Explanation:
\begin{aligned}
S.I. = \frac{1000*10*4}{100} = 400 \\
C.I. = [1000(1+\frac{10}{100})^4 - 1000] \\
= 464.10
\end{aligned}
So difference between simple interest and compound interest will be 464.10 - 400 = 64.10
4. Albert invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit.
- Rs. 8510
- Rs. 8620
- Rs. 8730
- Rs. 8820
Answer: Option D
Explanation:
\begin{aligned}
=> (8000 \times(1+\frac{5}{100})^2) \\
=> 8000 \times \frac{21}{20}\times \frac{21}{20} \\
=> 8820
\end{aligned}
5. If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what will be the compound interest on same values
- Rs.51.75
- Rs 51.50
- Rs 51.25
- Rs 51
Answer: Option C
Explanation:
\begin{aligned}
S.I. = \frac{P*R*T}{100} \\
P = \frac{50*100}{5*2} = 500\\
Amount = 500(1+\frac{5}{100})^2 \\
500(\frac{21}{20} * \frac{21}{20}) \\
= 551.25 \\
C.I. = 551.25 - 500 = 51.25
\end{aligned}
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