11. In certain years a sum of money is doubled itself at \(\displaystyle 6\frac{1}{4}\%\) simple interest per annum, then the required time will be
(a) \(\displaystyle 12\frac{1}{2}years\)
(b) 8 years
(c) \(\displaystyle 10\frac{2}{3}years\)
(d) 16 years
(e) None of these
Solution: (d)
Let x be the principal amount ‘y’ be the time to double the money. Then interest will also be ‘x’.
\(\displaystyle \Rightarrow \)x = \(\displaystyle \frac{{x\times 25\times y}}{{4\times 100}}\)
400 = 25y
y = 16 years
12. The difference between successive discounts of 40% followed by 30% and 45% followed by 20% on the marked price of an article is ₹ 12. The marked price of the article is:
13. A sum of ₹ 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of ₹ 362.50 more is lent but at the rate twice the former. At the end of the year, ₹ 33.50 is earned as interest from both the loans. What was the original rate of interest?
(a) 3.46%
(b) 3.6%
(c) 4.5%
(d) 5%
(e) None of these
Solution: (a)
Let the original rate be R%. Then, new rate = (2R)%
\(\displaystyle (\frac{{725\times R\times I}}{{100}})+(\frac{{362.50\times 2R\times I}}{{100\times 3}})=33.50\)
\(\displaystyle \Rightarrow \) \(\displaystyle (2175+725)R=3.50\times 100\times 3=10050\)
\(\displaystyle \Rightarrow \)R= \(\displaystyle \frac{{10050}}{{2900}}=3.46\%\)
14. A sum of money at simple interest amounts to ₹5852 in 3 years and ₹7788 in 7 years. What is the rate of interest per annum?
(a) 8%
(b) 9%
(c) 10%
(d) 11%
(e) 12%
Solution: (d)
Let sum = ₹ A and interest rate = r%
\(\displaystyle A+\frac{{A\times r\times 3}}{{100}}=5852\)
\(\displaystyle A[1+\frac{{3r}}{{100}}]=5852\) ——- (i)
\(\displaystyle A+\frac{{A\times r\times 7}}{{100}}=7788\)
\(\displaystyle A+\frac{{A\times r\times 7}}{{100}}=7788\) ——-(ii)
From equations (i) and (ii), r = 11%
15. What will be the difference between the interest accrued on a sum of ₹4500 at 12% per annum for 2 years and that on a sum of ₹ 5600 at 9% per annum for 2 years ?
16. Arun invested a sum of money at a certain rate of simple interest for a period of four years. Had he invested the same sum for a period of six years, the total interest earned by him would have been fifty per cent more than the earlier interest amount. What was the rate of interest per cent per annum?
(a) 4
(b) 8
(c) 5
(d) Cannot be determined
(e) None of these
Solution: (d)
According to the question,
\(\displaystyle \frac{{P\times R\times 6}}{{100}}=\frac{{P\times R\times 4}}{{100}}\times \frac{{150}}{{100}}\)
This type of relations gives n results, hence the answer is (d) Cannot be determined
17. A certain sum is invested for T years. It amounts to ₹ 400 at 10% per annum. But when invested at 4% per annum, it amounts to ₹ 200. Find the time (T)?
(a) 39 years
(b) 41 years
(c) 45 years
(d) 50 years
(e) None of these
Solution: (d)
We have, A1 = Rs. 400, A2 = ` 200, R1 = 10%, R2 =4%
Time (T)\(\displaystyle =[A1-A2]\times 100\) divide by \(\displaystyle A2R1-A1R2\)
\(\displaystyle \begin{array}{l}=\frac{{[400-200]\times 100}}{{[200\times 10-400\times 4]}}\\=\frac{{20000}}{{400}}=50Years\end{array}\)
18. Rakesh invests ₹ 12000 as fixed deposit at a bank at the rate of 10% per annum SI. But due to some pressing needs he has to withdraw the entire money after 3 years, for which the bank allowed him a lower rate of interest. If he gets ₹ 3320 less than what he would have got at the end of 5 years, the rate of interest allowed by the bank is
(a) \(\displaystyle \frac{{68}}{9}\%\)
(b) \(\displaystyle \frac{{64}}{9}\%\)
(c) \(\displaystyle \frac{{67}}{9}\%\)
(d) \(\displaystyle \frac{{61}}{9}\%\)
(e) None of these
Solution: (c)
P = 12000, T1=10 years, T2=3 years, R1=10%, R2=?
\(\displaystyle \left[ {\frac{{(12000\times 10\times 5)}}{{100}}-\frac{{(12000\times R2\times 3)}}{{100}}} \right]=3392\)
\(\displaystyle 50-3{{R}_{2}}=\frac{{83}}{3}\)
\(\displaystyle {{R}_{2}}=\frac{{67}}{9}\%\)
19. Riya saves an amount of 500 every year and then lent that amount at an interest of 10 percent compounded annually. Find the amount after 3 years.
(a) 1820.5
(b) 1840.5
(c) 1920.5
(d) 1940.5
(e) None of these
Solution: (a)
Total amount = \(\displaystyle 500\times {{(1+\frac{{10}}{{100}})}^{3}}+500{{(1+\frac{{10}}{{100}})}^{2}}+500(1+\frac{{10}}{{100}})=1820.5\)
20. A person invested part of ₹ 45000 at 4% and the rest at 6%. If his annual income from both are equal, then what is the average rate of interest?
(a) 4.6%
(b) 4.8%
(c) 5.0%
(d) 5.2%
(e) None of these
Solution: (b)
Let a person invest 4% of x.
According to question
\(\displaystyle \frac{{x\times 4}}{{100}}=\frac{{(45000-x)}}{{100}}\times 6\)
\(\displaystyle \Rightarrow \)2x = 45000 × 3 – 3x
\(\displaystyle \Rightarrow \)x = \(\displaystyle \frac{{45000\times 3}}{5}=27000\)
Another part is ₹ 18000.
Let r = Average rate of interest
Interest for 1st part in one year = \(\displaystyle \frac{{27000\times 4}}{{100}}=1080\)
Similarly, interest for rest part in one year = 1080
Total interest = ₹ 2160
\(\displaystyle \frac{{45000\times r}}{{100}}=2160\)
\(\displaystyle \Rightarrow \)\(\displaystyle r=\frac{{216}}{{45}}=4.8\%\)
