1. Mr. Khanna took a loan of 10,000 on simple interest for two years at the rate of 3 p.c.p.a. The total amount that he will be paying as interest in 2 years is 3% of his monthly salary. What is his monthly salary?
2. Mr. Nair’s monthly salary is ₹ 22,500. He took a loan of ₹ 30,000 on simple interest for 3 years at the rate of 5 p.c.p.a. The amount that he will be paying as simple interest in 3 years is what percent of his monthly salary?
(a) 10
(b) 18
(c) 20
(d) 25
(e) None of these
Solution: (c)
\(\displaystyle S.I.=\frac{{principal\times time\times rate}}{{100}}\)
= \(\displaystyle \frac{{30000\times 3\times 5}}{{100}}=4500\)
Let x % of 22500 % = 4500
\(\displaystyle \frac{{22500\times x}}{{100}}=4500\)
x = \(\displaystyle \frac{{4500\times 100}}{{22500}}=20\)
3. The simple interest accrued in 9 years on a principal of ₹24,250 is 162 percent of the principal. What is the rate of interest p.c.p.a.?
(a) 16
(b) 18
(c) 22
(d) Cannot be determined
(e) None of these
Solution: (b)
Interest = 162% of the principal
\(\displaystyle \frac{{SI}}{{\Pr incipal}}=\frac{{162}}{{100}}\)
\(\displaystyle Rate=\frac{{SI\times 100}}{{principal\times time}}=\frac{{162\times 100}}{{100\times 9}}\)
= 18% per annum
4. What would be the simple interest accrued in four years on a principle of ₹ 18,440 at the rate of 15 pcpa?
(a) ₹ 11.075
(b) ₹ 12.250
(c) ₹ 11.500
(d) ₹ 12.985
(e) None of these
Solution: (e)
SI = \(\displaystyle \frac{{p\times r\times t}}{{100}}=\frac{{18440\times 15\times 4}}{{100}}=11064\)
5. What would be the simple interest accrued in 4 years on a principal of ₹16,500 at the rate of 16 p.c.p.a.?
6. Mr X invested a certain amount in Debt and Equity Funds in the ratio of 4 : 5. At the end of one year, he earned a total dividend of 30% on his investment. After one year, he reinvested the amount including the dividend in the ratio of 6 : 7 in Debt and Equity Funds. If the amount reinvested in Equity Funds was ₹94,500, what was the original amount invested in Equity Funds?
(a) ₹75,000
(b) ₹81,000
(c) ₹60,000
(d) ₹65,000
(e) None of these
Solution: (a)
Amount reinvested in debt + Equity Funds
= \(\displaystyle 94500\times \frac{{13}}{7}=175500\)
Amount invested earlier in Debt + Equity Funds
= \(\displaystyle \frac{{175500}}{{1.3}}=135000\)
Original amount invested in equity funds
= \(\displaystyle \frac{5}{9}\times 135000=75000\)
7. A person invested in all ₹ 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is:
(a) ₹ 200
(b) ₹ 600
(c) ₹ 800
(d) ₹ 1200
(e) None of these
Solution: (d)
Let the parts be x, y and [2600 – (x + y)]. Then,
\(\displaystyle \frac{{x\times 4\times 1}}{{100}}=\frac{{y\times 6\times 1}}{{100}}=\frac{{[2600-(x-y)]\times 8\times 1}}{{100}}\)
\(\displaystyle \frac{y}{x}=\frac{4}{6}=\frac{2}{3}ory=\frac{2}{3}x\)
So , \(\displaystyle \frac{{x\times 4\times 1}}{{100}}=\frac{{(2600-\frac{5}{3}x)\times 8}}{{100}}\)
\(\displaystyle \Rightarrow \)4x= \(\displaystyle \frac{{(7800-5x)\times 8}}{3}\)
\(\displaystyle \Rightarrow \)52x=(7800×8)
\(\displaystyle \Rightarrow \)x = \(\displaystyle \frac{{7800\times 8}}{{52}}=1200\)
Therefore, Money invested at 4% = ₹ 1200.
8. In how many years will ₹ 4600 amount to ₹ 5428 at 3 p.c.p.a. simple interest?
9. A sum of ₹ 2200 is invested at two different rates of interest. The difference between the interests got after 4 years is ₹ 202.40. What is the difference between the rates of interest ?
(a) 3.3%
(b) 2.3%
(c) 3.5%
(d) 2.5%
(e) None of these
Solution: (b)
Let R1 and R2 be the two different rate of interest, where \(\displaystyle {{R}_{1}}>{{R}_{2}}\)
\(\displaystyle \frac{{2200\times {{R}_{1}}\times 4}}{{100}}-\frac{{2200\times {{R}_{2}}\times 4}}{{100}}=202.40\)
\(\displaystyle \frac{{2200\times 4}}{{100}}[{{R}_{1}}-{{R}_{2}}]=202.40\)
\(\displaystyle {{R}_{1}}-{{R}_{2}}=\frac{{202.40\times 100}}{{2200\times 4}}=\frac{{50.6}}{{22}}\)
R1– R2 = 2.3%
10. An amount of ₹ 1,00,000 is invested in two types of shares. The first yields an interest of 9% p.a. and the second, 11% p.a. If the total interest at the end of one year is \(\displaystyle 9\frac{3}{4}\%\) then the amount invested in each share was:
(a) ₹ 52,500; ₹ 47,500
(b) ₹ 62, 500; ₹ 37,500
(c) ₹ 72,500: ₹ 27,500
(d) ₹ 82, 500; ₹ 17,500
(e) None of these
Solution: (b)
Let the sum invested at 9% be ₹ x and that invested at 11% be ₹ (100000 – x).
Then, \(\displaystyle (\frac{{x\times 9\times 1}}{{100}})+[\frac{{(100000-x)\times 11\times 1}}{{100}}]\)
= \(\displaystyle (100000\times \frac{{39}}{4}\times \frac{1}{{100}})\)
\(\displaystyle \frac{{9x+1100000-11x}}{{100}}=\frac{{39000}}{4}=9750\)
\(\displaystyle \Rightarrow \)2x = (1100000 – 975000) = 125000 x = 62500.
\(\displaystyle \Rightarrow \)Sum invested at 9% = ₹ 62500.
Sum invested at 11% = ₹ (100000 – 62500) = ₹ 37500.
